Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of m...The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of motion for the system was set up by using Liapunov's first approximation theory. Based on the theory of Noether symmetry,the Liapunov's function was constructed,and the criterion of stability of motion for the system was also set up by using Liapunov's direct method. Two examples were given to illustrate the application of the results.展开更多
Human activities, such as blasting excavation, bolting, grouting and impounding of reservoirs, will lead to disturbances to rock masses and variations in their structural features and material properties. These engine...Human activities, such as blasting excavation, bolting, grouting and impounding of reservoirs, will lead to disturbances to rock masses and variations in their structural features and material properties. These engineering disturbances are important factors that would alter the natural evolutionary processes or change the multi-field interactions in the rock masses from their initial equilibrium states. The concept of generalized multi-field couplings was proposed by placing particular emphasis on the role of engineering disturbances in traditional multi-field couplings in rock masses. A mathematical model was then developed, in which the effects of engineering disturbances on the coupling-processes were described with changes in boundary conditions and evolutions in thermo-hydro-mechanical （THM） properties of the rocks. A parameter, d, which is similar to damage variables but has a broader physical meaning, was conceptually introduced to represent the degree of engineering disturbances and the couplings among the material properties. The effects of blasting excavation, bolting and grouting in rock engineering were illustrated with various field observations or theoretical results, on which the degree of disturbances and the variations in elastic moduli and permeabilities were particularly focused. The influences of excavation and groundwater drainage on the seepage flow and stability of the slopes were demonstrated with numerical simulations. The proposed approach was further employed to investigate the coupled hydro-mechanical responses of a high rock slope to excavation, bolting and impounding of the reservoir in the dam left abutment of Jinping I hydropower station. The impacts of engineering disturbances on the deformation and stability of the slope during construction and operation were demonstrated.展开更多
The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may j...The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining.Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability,but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies.A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions.Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and threedimensional failure mechanisms.This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion.Moreover,the proposed model includes the effect of seismic forces,which are not always taken into account in slope stability analyses.The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.展开更多
Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures,which are closely determined by the processing routes,such as phase transformations(PTs)and plastic ...Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures,which are closely determined by the processing routes,such as phase transformations(PTs)and plastic deformations(PDs).Both PTs and PDs follow inherent trade-off relation between thermodynamic driving force ΔG and kinetic energy barrier Q,i.e.,so-called thermo-kinetic correlation.By analyzing nucleation and growth and proposing a conception of negative driving force integrating strain energy,interface energy and any kind of energy that equivalently inhibits the PT itself,ΔG^(S),unified expressions for the thermo-kinetic correlation and generalized stability(GS)were derived for three kinds of PTs,i.e.,diffusive PTs with simultaneously decreasedΔG and increased Q,diffusive PTs with simultaneously increasedΔG and decreased Q,and displacive PTs with simultaneously increased ΔG and decreased Q.This leads to so-called thermo-kinetic connectivity by integrating the thermo-kinetic correlation and the GS,where,by application in typical PTs,it was clearly shown,a criterion of high ΔG-high GS can be predicted by modulating chemical driving force,negative driving force and kinetic energy barrier for diffusion or nucleation.Following thermo-kinetic connectivity,analogous procedure for dislocation evolution upon PDs was performed,and materials design in terms of the highΔG-high GS criterion was discussed and prospected.展开更多
Macro-and micro-segregation formed upon twin-roll casting(TRC)can be inherited from sub-rapid solid-ification to solid-state transformation,even to plastic deformation,thus deteriorating drastically mechan-ical proper...Macro-and micro-segregation formed upon twin-roll casting(TRC)can be inherited from sub-rapid solid-ification to solid-state transformation,even to plastic deformation,thus deteriorating drastically mechan-ical properties of as-produced thin sheets.Although many works focusing mainly on controlling fields of thermal,concentration and convection have been reported,how to control artificially and quantitatively the segregation using a theoretical connection between processing parameters and solidification models,has not been realized,yet.Regarding it,a systematical framework integrating non-equilibrium dendritic growth and overall solidification kinetics with the TRC parameters,was constructed applying a general-ized stability(GS)conception deduced from transient thermodynamic driving force△G^(t)and transient ki-netic energy barrier Q_(eff)^(t)evolving upon solidification.Departing from this framework considering synergy of thermodynamics and kinetics(i.e.,thermo-kinetic synergy),a criterion of high△G^(t)-high GS guaranteed that the macro(i.e.,the centerline)and the micro(i.e.,the edge)segregation can be suppressed by in-creasing△G^(t)and GS at the beginning and the ending stage of sub-rapid solidification,respectively.This typical thermo-kinetic combination producing the microstructure can be inherited into the plastic de-formation,as reflected by corresponding strength-ductility combinations.This work realized quantitative controlling of TRC by a theoretical connection between processing parameters and solidification models,where,an optimization for sub-rapid solidification segregation using the GS conception including△G^(t)and Q_(eff)^(t)has been performed.展开更多
The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layeris constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol'd'...The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layeris constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol'd'svariational principle and a prior estimate method. The nonlinear stability criteria are established. For comparison, the linear instability criteria are also obtained by using normal mode method. and the influences ofthe free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear instability are discussed by use of the growth rate curves. The comparison between the nonlinear stability criterion and the linear one is made. It is shown that insome cases the two criteria are exactly the same in form, but in other cases, they are different. This phenomenon, which reveals the nonlinear property of the linear instability features. is explained by the explosiveresonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role inthe dynamical system. the nonlinear stability criterion is different from the linear one, on the other hand.when there does not exist the ERI. the nonlinear stability criterion is the same as the linear one in form.展开更多
This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth c...This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].展开更多
In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.展开更多
In this paper,a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of orderα(1<α<2)are given.The main results are obtained b...In this paper,a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of orderα(1<α<2)are given.The main results are obtained by using Krasnoselskii's fixed point theorem in a weighted Banach space.Two examples are given to demonstrate the validity of the proposed results.展开更多
This paper studies the system stability problems of a class of nonconvex differential inclusions.At first,a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions.Moreover,a ge...This paper studies the system stability problems of a class of nonconvex differential inclusions.At first,a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions.Moreover,a generalized invariance principle and related attraction conditions are proposed and proved to overcome the technical difficulties due to the absence of convexity.In the technical analysis,a novel set-valued derivative is proposed to deal with nonsmooth systems and nonsmooth Lyapunov functions.Additionally,the obtained results are consistent with the existing ones in the case of convex differential inclusions with regular Lyapunov functions.Finally,illustrative examples are given to show the effectiveness of the methods.展开更多
The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given...The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.展开更多
This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Go...This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.展开更多
Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Lan...In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov展开更多
Inner stability and stabilization of Cohen-Grossberg generalized delay stochastic neural network with distributed parameter are discussed. The main method adopted is, combining inequality techniques, to apply Ito diff...Inner stability and stabilization of Cohen-Grossberg generalized delay stochastic neural network with distributed parameter are discussed. The main method adopted is, combining inequality techniques, to apply Ito differential formula to the constructed average function with respect to spatial variables along the system considered under the integral operator. Some sufficient conditions are given.展开更多
In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approx...In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.展开更多
Multi-layer slopes are widely found in clay residue receiving fields.A generalized horizontal slice method(GHSM)for assessing the stability of multi-layer slopes that considers the energy dissipation between adjacent ...Multi-layer slopes are widely found in clay residue receiving fields.A generalized horizontal slice method(GHSM)for assessing the stability of multi-layer slopes that considers the energy dissipation between adjacent horizontal slices is presented.In view of the upper-bound limit analysis theory,the energy equation is derived and the ultimate failure mode is generated by comparing the sliding surface passing through the slope toe(mode A)with that below(mode B).In addition,the influence of the number of slices on the stability coefficients in the GHSM is studied and the stable value is obtained.Compared to the original method(Chen’s method),the GHSM can acquire more precise results,which takes into account the energy dissipation in the inner sliding soil mass.Moreover,the GHSM,limit equilibrium method(LEM)and numerical simulation method(NSM)are applied to analyze the stability of a multi-layer slope with different slope angles and the results of the safety factor and failure mode are very close in each case.The ultimate failure modes are shown to be mode B when the slope angle is not more than 28°.It illustrates that the determination of the ultimate sliding surface requires comparison of multiple failure modes,not only mode A.展开更多
In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been...In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
基金Sponsored by the National Natural Science Foundation of China( 10972151)the Natural Science Foundation of Higher Education Institution of Jiangsu Province,China ( 08KJB130002)
文摘The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of motion for the system was set up by using Liapunov's first approximation theory. Based on the theory of Noether symmetry,the Liapunov's function was constructed,and the criterion of stability of motion for the system was also set up by using Liapunov's direct method. Two examples were given to illustrate the application of the results.
基金Supported by the National Natural Science Fund for Distinguished Young Scholars of China(50725931)the National Natural Science Foundation of China(50839004,51079107)the Supporting Program of the "Eleventh Five-year Plan" for Sci & Tech Research of China(2008BAB29B01)
文摘Human activities, such as blasting excavation, bolting, grouting and impounding of reservoirs, will lead to disturbances to rock masses and variations in their structural features and material properties. These engineering disturbances are important factors that would alter the natural evolutionary processes or change the multi-field interactions in the rock masses from their initial equilibrium states. The concept of generalized multi-field couplings was proposed by placing particular emphasis on the role of engineering disturbances in traditional multi-field couplings in rock masses. A mathematical model was then developed, in which the effects of engineering disturbances on the coupling-processes were described with changes in boundary conditions and evolutions in thermo-hydro-mechanical （THM） properties of the rocks. A parameter, d, which is similar to damage variables but has a broader physical meaning, was conceptually introduced to represent the degree of engineering disturbances and the couplings among the material properties. The effects of blasting excavation, bolting and grouting in rock engineering were illustrated with various field observations or theoretical results, on which the degree of disturbances and the variations in elastic moduli and permeabilities were particularly focused. The influences of excavation and groundwater drainage on the seepage flow and stability of the slopes were demonstrated with numerical simulations. The proposed approach was further employed to investigate the coupled hydro-mechanical responses of a high rock slope to excavation, bolting and impounding of the reservoir in the dam left abutment of Jinping I hydropower station. The impacts of engineering disturbances on the deformation and stability of the slope during construction and operation were demonstrated.
文摘The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining.Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability,but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies.A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions.Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and threedimensional failure mechanisms.This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion.Moreover,the proposed model includes the effect of seismic forces,which are not always taken into account in slope stability analyses.The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.
基金the National Key R&D Program of China(No.2017YFB0703001)the National Natural Science Foundation of China(Nos.52130110,51790481,51901182 and 51901185)the Natural Science Foundation of Shaanxi Province(Nos.2020JQ-157 and 2020JQ-153)。
文摘Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures,which are closely determined by the processing routes,such as phase transformations(PTs)and plastic deformations(PDs).Both PTs and PDs follow inherent trade-off relation between thermodynamic driving force ΔG and kinetic energy barrier Q,i.e.,so-called thermo-kinetic correlation.By analyzing nucleation and growth and proposing a conception of negative driving force integrating strain energy,interface energy and any kind of energy that equivalently inhibits the PT itself,ΔG^(S),unified expressions for the thermo-kinetic correlation and generalized stability(GS)were derived for three kinds of PTs,i.e.,diffusive PTs with simultaneously decreasedΔG and increased Q,diffusive PTs with simultaneously increasedΔG and decreased Q,and displacive PTs with simultaneously increased ΔG and decreased Q.This leads to so-called thermo-kinetic connectivity by integrating the thermo-kinetic correlation and the GS,where,by application in typical PTs,it was clearly shown,a criterion of high ΔG-high GS can be predicted by modulating chemical driving force,negative driving force and kinetic energy barrier for diffusion or nucleation.Following thermo-kinetic connectivity,analogous procedure for dislocation evolution upon PDs was performed,and materials design in terms of the highΔG-high GS criterion was discussed and prospected.
基金support of the Natural Science Foundation of China(Nos.51790481,51790483,52130110,51901182)the Natural Science Foundation of Shaanxi Province(No.2020JQ-157)+1 种基金the Foundation of State Key Laboratory of Rolling and Automation(No.2020RALKFKT001)the Research Fund of the State Key Laboratory of Solidification Processing(No.2022-TS-01).
文摘Macro-and micro-segregation formed upon twin-roll casting(TRC)can be inherited from sub-rapid solid-ification to solid-state transformation,even to plastic deformation,thus deteriorating drastically mechan-ical properties of as-produced thin sheets.Although many works focusing mainly on controlling fields of thermal,concentration and convection have been reported,how to control artificially and quantitatively the segregation using a theoretical connection between processing parameters and solidification models,has not been realized,yet.Regarding it,a systematical framework integrating non-equilibrium dendritic growth and overall solidification kinetics with the TRC parameters,was constructed applying a general-ized stability(GS)conception deduced from transient thermodynamic driving force△G^(t)and transient ki-netic energy barrier Q_(eff)^(t)evolving upon solidification.Departing from this framework considering synergy of thermodynamics and kinetics(i.e.,thermo-kinetic synergy),a criterion of high△G^(t)-high GS guaranteed that the macro(i.e.,the centerline)and the micro(i.e.,the edge)segregation can be suppressed by in-creasing△G^(t)and GS at the beginning and the ending stage of sub-rapid solidification,respectively.This typical thermo-kinetic combination producing the microstructure can be inherited into the plastic de-formation,as reflected by corresponding strength-ductility combinations.This work realized quantitative controlling of TRC by a theoretical connection between processing parameters and solidification models,where,an optimization for sub-rapid solidification segregation using the GS conception including△G^(t)and Q_(eff)^(t)has been performed.
文摘The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layeris constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol'd'svariational principle and a prior estimate method. The nonlinear stability criteria are established. For comparison, the linear instability criteria are also obtained by using normal mode method. and the influences ofthe free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear instability are discussed by use of the growth rate curves. The comparison between the nonlinear stability criterion and the linear one is made. It is shown that insome cases the two criteria are exactly the same in form, but in other cases, they are different. This phenomenon, which reveals the nonlinear property of the linear instability features. is explained by the explosiveresonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role inthe dynamical system. the nonlinear stability criterion is different from the linear one, on the other hand.when there does not exist the ERI. the nonlinear stability criterion is the same as the linear one in form.
基金supported by the National Natural Science Foundation of China(11401122)Science and technology project of Qufu Normal University(xkj201607)
文摘This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu ＋uxx = uv ＋ ｜u｜^2u, vtt-vxx=（｜u｜^2）xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].
文摘In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.
文摘In this paper,a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of orderα(1<α<2)are given.The main results are obtained by using Krasnoselskii's fixed point theorem in a weighted Banach space.Two examples are given to demonstrate the validity of the proposed results.
基金This work was supported by the geijing Natural Science Foundation(No.4152057)the Natural Science Foundation of China(Nos.61333001,61573344)the China Postdoctoral Science Foundation(No.2015M581190).
文摘This paper studies the system stability problems of a class of nonconvex differential inclusions.At first,a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions.Moreover,a generalized invariance principle and related attraction conditions are proposed and proved to overcome the technical difficulties due to the absence of convexity.In the technical analysis,a novel set-valued derivative is proposed to deal with nonsmooth systems and nonsmooth Lyapunov functions.Additionally,the obtained results are consistent with the existing ones in the case of convex differential inclusions with regular Lyapunov functions.Finally,illustrative examples are given to show the effectiveness of the methods.
基金supported by the National Natural Science Foundation of China(No.11972241)the Natural Science Foundation of Jiangsu Province (No.BK20191454)the Scientific Research Foundation of Suzhou University of Science and Technology (No.XKZ2017005)。
文摘The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.
文摘This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.
基金Project supported by the Tianyuan Foundation of National Natural Science of China(No.11126079)the China Postdoctoral Science Foundation(No.2013M530559)the Fundamental Research Funds for the Central Universities(No.CDJRC10100011)
文摘Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
基金The research is supported by the Scientific Research Foundation of Yunnan Provincial Departmentthe Natural Science Foundation of Yunnan Province(No.2005A0026M).
文摘In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov
文摘Inner stability and stabilization of Cohen-Grossberg generalized delay stochastic neural network with distributed parameter are discussed. The main method adopted is, combining inequality techniques, to apply Ito differential formula to the constructed average function with respect to spatial variables along the system considered under the integral operator. Some sufficient conditions are given.
文摘In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.
基金support provided by the National Key R&D Program of China(No.2017YFC1501304)the National Natural Science Foundation of China(Nos.42090054,41922055 and 41931295)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(No.CUGGC09).
文摘Multi-layer slopes are widely found in clay residue receiving fields.A generalized horizontal slice method(GHSM)for assessing the stability of multi-layer slopes that considers the energy dissipation between adjacent horizontal slices is presented.In view of the upper-bound limit analysis theory,the energy equation is derived and the ultimate failure mode is generated by comparing the sliding surface passing through the slope toe(mode A)with that below(mode B).In addition,the influence of the number of slices on the stability coefficients in the GHSM is studied and the stable value is obtained.Compared to the original method(Chen’s method),the GHSM can acquire more precise results,which takes into account the energy dissipation in the inner sliding soil mass.Moreover,the GHSM,limit equilibrium method(LEM)and numerical simulation method(NSM)are applied to analyze the stability of a multi-layer slope with different slope angles and the results of the safety factor and failure mode are very close in each case.The ultimate failure modes are shown to be mode B when the slope angle is not more than 28°.It illustrates that the determination of the ultimate sliding surface requires comparison of multiple failure modes,not only mode A.
文摘In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.
