In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which ...In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.展开更多
In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function i...In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.展开更多
We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and te...We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantu...托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantum esse,being as beinginjeneral)。他在论证是自身时强调实在意义上的是重于逻辑意义的是。是(being)包括本质(essence)与存在(existence);本质(essence)与存在(existence)皆为是者(beings)。而存在(existence)先于本质(essence);存在(existence)是是(being)之最具体的、个别的、实体的、独一无二的完美实现(act)。托马斯.阿奎那的存在论哲学颠覆了传统哲学中存在与本质的位置,它以一种存在主义代替本质主义,从而在形而上学历史上掀起一场革命。展开更多
Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the...Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions展开更多
In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh...In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.展开更多
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0...The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.展开更多
Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact con...Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.展开更多
In this paper,our main goal is to study a new mathematical model which describes the frictional contact between a foundation and a deformable body which is composed of viscoplastic materials and where the process is c...In this paper,our main goal is to study a new mathematical model which describes the frictional contact between a foundation and a deformable body which is composed of viscoplastic materials and where the process is considered dynamic.The contact condition on the normal plane is modeled by a unilateral constraint condition for a version of normal velocity in which the memory effect and the adhesion are considered.On the tangential plane a frictional contact condition is governed by the Clarke subdifferential of a locally Lipschitz function,and the evolution of the bonding field is governed by an ordinary differential equation.We formulate this problem as coupled system that consists of two ordinary differential equations and a variational-hemivariational inequality.Then,the existence,uniqueness and continuous dependence of the solution on the data results concerning the abstract system are established.Finally,we use the abstract results to show the existence and uniqueness of the solution to the contact problem.展开更多
China English is an objective existence as a performance variety used in China.It is based on standard English and possesses Chinese characteristics.The Chinese characteristics of China English are reflected in the ph...China English is an objective existence as a performance variety used in China.It is based on standard English and possesses Chinese characteristics.The Chinese characteristics of China English are reflected in the phonology,vocabulary,syntax,rhetoric and text,particularly in the vocabulary.This essay will discuss the features of China English from the following three aspects: the development of English in China;the comparison between China English,Pidgin English and Chinese English and the Chinese words borrowed by English.展开更多
This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive in...This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.展开更多
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ...Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.展开更多
By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam w...By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.展开更多
In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potentia...In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
In this paper,Cauchy problem of viscous Cahn-Hilliard equation with inertial term in multi-space dimension is considered.Based on the detailed analysis of Green function,using fixed point theorem,we get the global in-...In this paper,Cauchy problem of viscous Cahn-Hilliard equation with inertial term in multi-space dimension is considered.Based on the detailed analysis of Green function,using fixed point theorem,we get the global in-time existence of classical solution.Furthermore,we get Lp decay rate of the solution.展开更多
In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed po...In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed point theorem, Banach contraction principle and Ulam type stability.展开更多
This paper addresses the existence detection of blanket jamming based on fractal features in fractional Fourier transform (FRET) domain. Firstly, the existences of fractal features of three typical jamming signals are...This paper addresses the existence detection of blanket jamming based on fractal features in fractional Fourier transform (FRET) domain. Firstly, the existences of fractal features of three typical jamming signals are analyzed, and box dimension and information dimension are employed to describe fractal features quantitatively. Then the differences of fractal characteristics between blanket jamming and white Gaussian noise (WGN) in FRFT domain are described, and a detector to detect the jamming is proposed. At last, simulations are done to verify that the algorithm is effective preferable.展开更多
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金supported by the Project for Outstanding Young Talents in Bagui of Guangxi,the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NSFC(12371312)+2 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the Postdoctoral Fellowship Program of CPSF(GZC20241534)the Startup Project of Postdoctoral Scientific Research of Zhejiang Normal University(ZC304023924).
文摘In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.
文摘In this paper,we study the weighted higher order semilinear equation in an exterior domain(-△)^(m)u=|x|^(α)g(u)in R^(N)\B_(R_(0)),where N≥1,m≥2 are integers,α>-2m,g is a continuous and nondecreasing function in(0,+∞)and positive in(0,+∞),B_(R_(0))is the ball of the radius R0 centered at the origin.We prove that a positive supersolution of the problem which verifies(-△)_(i)u>0 in R^(N)\B_(R_(0))(i=0,…,m-1)exists if and only if N>2m and∫_(0)^(δ)g(t)/t^(2(N-m)+α/N-2m)dt<∞,,for someδ>0.We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when g(u)=u^(p)with p>1,by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces.
文摘We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantum esse,being as beinginjeneral)。他在论证是自身时强调实在意义上的是重于逻辑意义的是。是(being)包括本质(essence)与存在(existence);本质(essence)与存在(existence)皆为是者(beings)。而存在(existence)先于本质(essence);存在(existence)是是(being)之最具体的、个别的、实体的、独一无二的完美实现(act)。托马斯.阿奎那的存在论哲学颠覆了传统哲学中存在与本质的位置,它以一种存在主义代替本质主义,从而在形而上学历史上掀起一场革命。
文摘Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions
文摘In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.
文摘The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.
基金The National Natural Science Foundation of China(No.10672039)the Key Project of Ministry of Education of China(No.105083)
文摘Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.
基金supported by the NSF of Shanxi(202303021221168)the Industry-university-research project of Shanxi Datong University(2022CXY10,2022CXY13).
文摘In this paper,our main goal is to study a new mathematical model which describes the frictional contact between a foundation and a deformable body which is composed of viscoplastic materials and where the process is considered dynamic.The contact condition on the normal plane is modeled by a unilateral constraint condition for a version of normal velocity in which the memory effect and the adhesion are considered.On the tangential plane a frictional contact condition is governed by the Clarke subdifferential of a locally Lipschitz function,and the evolution of the bonding field is governed by an ordinary differential equation.We formulate this problem as coupled system that consists of two ordinary differential equations and a variational-hemivariational inequality.Then,the existence,uniqueness and continuous dependence of the solution on the data results concerning the abstract system are established.Finally,we use the abstract results to show the existence and uniqueness of the solution to the contact problem.
文摘China English is an objective existence as a performance variety used in China.It is based on standard English and possesses Chinese characteristics.The Chinese characteristics of China English are reflected in the phonology,vocabulary,syntax,rhetoric and text,particularly in the vocabulary.This essay will discuss the features of China English from the following three aspects: the development of English in China;the comparison between China English,Pidgin English and Chinese English and the Chinese words borrowed by English.
文摘This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.
文摘Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
文摘By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.
文摘In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
基金Supported by the National Natural Science Foundation of China(11571092)
文摘In this paper,Cauchy problem of viscous Cahn-Hilliard equation with inertial term in multi-space dimension is considered.Based on the detailed analysis of Green function,using fixed point theorem,we get the global in-time existence of classical solution.Furthermore,we get Lp decay rate of the solution.
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,Saudi Arabia under grant no.KEP-Msc-9-130-39
文摘In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed point theorem, Banach contraction principle and Ulam type stability.
基金supported by Key Laboratory of Science and Technology in Complex Electromagnetic Environment(201E-05-1)
文摘This paper addresses the existence detection of blanket jamming based on fractal features in fractional Fourier transform (FRET) domain. Firstly, the existences of fractal features of three typical jamming signals are analyzed, and box dimension and information dimension are employed to describe fractal features quantitatively. Then the differences of fractal characteristics between blanket jamming and white Gaussian noise (WGN) in FRFT domain are described, and a detector to detect the jamming is proposed. At last, simulations are done to verify that the algorithm is effective preferable.
