The performance of Mg alloys is significantly influenced by the concentrations and solid solution behavior of the alloying elements.In this work,the solid solution behavior of 20 alloying elements in 190 ternary Mg al...The performance of Mg alloys is significantly influenced by the concentrations and solid solution behavior of the alloying elements.In this work,the solid solution behavior of 20 alloying elements in 190 ternary Mg alloy systems at 500℃are systematically investigated.The solid solution behavior of a set of two different alloying elements in Mg alloy systems are suggested to be classified into three categories:inclusivity,exclusivity and proportionality.Inclusivity classification indicates that the two alloying elements are inclusive inα-Mg,increasing the joint solubility of both elements.Exclusivity classification suggests that the two alloying elements have a low joint solid solubility inα-Mg,since they prefer to form stable second phases.For the proportionality classification,the solubility curve of the ternary Mg alloy systems is a straight line connecting the solubility points of the two sub-binary systems.The proposed classification theory was validated by key experiments and the calculation of formation energies.The interaction effects between alloying elements and the preference of formation of second phases are the main factors determining the solid solution behavior classifications.Based on the observed solid solution features of multi-component Mg alloys,principles for alloy design of different types of high-performance Mg alloys were proposed in this work.展开更多
Solvents have an essential association with polymer solution behavior.However,few researches have been deeply done on this respect.In recent years,our research group focus on the study on effect of solvent properties ...Solvents have an essential association with polymer solution behavior.However,few researches have been deeply done on this respect.In recent years,our research group focus on the study on effect of solvent properties on solution behavior and film condensed state structure for semi-rigid conjugated polymer up till to apply for optoelectronic device.Herein,influence of solvent properties including solubility of solvent,aromaticity,polarity and hydrogen bonds on semi-rigid polymer chain solution behavior,i.e.,single chain conformation,chain shape,size and chains aggregated density were studied by means of static/dynamic laser light scattering(DLS/SLS)and exponential law etc.Effect of solvent properties on condensed state structure of the semi-rigid conjugated polymer film was studied by UV absorption spectroscopy,PL spectroscopy and electron microscopy etc.The essential reasons for the influence were discovered and the mechanism was revealed.It was found that solution behavior with different solvent properties had an essential physical relationship with chains condensed state structure of the semi-rigid conjugated polymers.More importantly,there was a quantitative structure-activity relationship between solution and film.The key to this relationship depended on the interaction between solvent molecules and the semi-rigid conjugated polymer chains.This interaction could also affect optoelectronic devices performance.This study is of great significance to effectively control the condensed state structure of the semirigid conjugated polymers in the process of dynamic evolution from solutions to films.It not only enriches the knowledge and understanding of both semi-rigid conjugated polymer solution behaviors and film condensed state physics based on polymer physics,but also is meaningful to practical application for conjugated polymer and other traditional polymer systems.展开更多
The solventnatures are crucial to deeply reveal solution behavior of macromolecular chains,physical essence of condensed state structures formation of the film as well as the photoelectronic devices performance.Based ...The solventnatures are crucial to deeply reveal solution behavior of macromolecular chains,physical essence of condensed state structures formation of the film as well as the photoelectronic devices performance.Based on the second virial coefficient(A2),effect of the synergistic action of solvents and external electric field on both solution behavior and the film’s condensed state structure for the semi-rigid conjugated polymer,poly[2-methoxy-5-(2’-ethylhexoxy)-1,4-phenylvinylene](MEH-PPV)was investigated by dynamic/static light scattering,photoluminescence spectroscopy and transmission electron microscopy,etc.It was found that although the MEH-PPV solutions with different solvents(toluene,chlorobenzene,chloroform and tetrahydrofuran)all could generate a response to the external electric field,the degree of response varied significantly with the change of solvent nature.Furthermore,ordered degree of the film from the solutions was also obviously different.The essential reason for this responsive difference was firstly revealed in the research,which actually depended on the degree of interaction between the solute and solvent,and this degree of interaction could be quantitatively described by the second virial coefficient(A2).The bigger the A2,the stronger the interaction between solvent and solute in the solution,and the stronger the response to the external electric field.Further,under the induction of external electric field,chains aggregations with different sizes were formed accompanied by large-scale chains ordered structure in the solution.This ordered structure not only can effectively transfer to film prepared by the precursor solution but also is beneficial to enhance the carrier mobility and device efficiency of the photoelectronic film.展开更多
This paper deals with reaction-diffusion system with nonlocal source. It is proved that there exists a unique classical solution and the solution either exists globally or blows up in finite time. Furthermore, its blo...This paper deals with reaction-diffusion system with nonlocal source. It is proved that there exists a unique classical solution and the solution either exists globally or blows up in finite time. Furthermore, its blow-up set and asymptotic behavior are obtained provided that the solution blows up in finite time.展开更多
Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) ...Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.展开更多
By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in g...By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.展开更多
A novel amphiphile of 4-[4-(4-decyloxyphenylazo) naphthyloxy] butyl trimethylammonium bromide has been synthesized. It can form the stable bilayer in dilute aqueous solution.
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions for [GRAPHICS] and for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the ex...The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions for [GRAPHICS] and for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the existence is reduced.展开更多
Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J...Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J） Sufficient and necessary conditions for （E）, （I） and （J） to have asymptotic stability of the gobal smooth solution are given by means of the elemental L2 energy method.展开更多
A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained b...A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained by Ladas, Sficas and Gopalsamy.展开更多
We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particu...We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particular, the double peakon solutions of both equations are investigated in detail. At the same time, the dynamic behaviors of three types double peakon solutions are analyzed by some figures.展开更多
This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink s...This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.展开更多
In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,ap...In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,apriori evaluations for this function are obtained.Then,by imposing some conditions on the function on the right-hand side of the equation and using appropriate inequalities,it is shown that the solution is asymptotically damped.展开更多
A controlled cross-linking polymerization containing intra- and intermolecular reactions was designed based on random coil morphology of macromolecules in solution. The soluble intramolecular cross-linked maeromolecu...A controlled cross-linking polymerization containing intra- and intermolecular reactions was designed based on random coil morphology of macromolecules in solution. The soluble intramolecular cross-linked maeromolecule （ICM） was successfully synthesized in the system with PVA and MDI. We found an especial dissolving phenomenon, namely the semi-soluble phenomenon when some gels dissolved in DMF. The chain growth process of ICMs was investigated by Transmission electron microscopy （TEM） pictures of samples at different reacting times, in addition, TEM pictures show ICMs have three kinds of styles in structure, viz. ＂globule structure＂, ＂nubby structure＂ and the intervenient between the above two structures, and the efflux time of the ICMs was measured by an Ubbelohde viscosimeter, it was found that the efflux time decreases with the degree ofcrosslink increasing.展开更多
This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichl...This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1.展开更多
This paper is concerned with the asymptotic behavior of solution to the following model involving two species all with chemotaxis：{αp/αt=Dp△（p△lnp/w）,αp/αt=Dq△（q△lnq/w）,αw/αt=βp-δw,p△ln（p/w）.^-n=q...This paper is concerned with the asymptotic behavior of solution to the following model involving two species all with chemotaxis：{αp/αt=Dp△（p△lnp/w）,αp/αt=Dq△（q△lnq/w）,αw/αt=βp-δw,p△ln（p/w）.^-n=q△ln（q/w）.^-n=0.We prove that the solution exists globally asβ ≥ 0. Asβ 〈 0, whether the solution exists globally or not depends on the initial data. By function transformation and compari- son, the asymptotical behavior of the solution is studied.展开更多
In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the soluti...In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the solutions to the equation are some high order of infinities,and also that some conditions which guarantee that every oscillatory solution to the equation has the property that the i order L operator of it tends to infinity when its independent variable tends to zero.展开更多
IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M<sub>1<...IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M<sub>1</sub>, M<sub>2</sub> and M<sub>3</sub> which can react with each other to produce two new kinds of other chemical compounds: （M<sub>2</sub>）<sub>n</sub> （M<sub>1</sub>）<sub>m</sub> and （M<sub>3</sub>）<sub>r</sub> （M<sub>1</sub>）<sub>κ</sub> at the same time. Usually, these reactions are irreversible and they have the following forms:展开更多
We study the long-time behavior of viscosity solutions for time-dependent Hamilton-Jacobi equations by the dynamical approach based on weak KAM(Kolmogorov-Arnold-Moser) theory due to Fathi. We establish a general conv...We study the long-time behavior of viscosity solutions for time-dependent Hamilton-Jacobi equations by the dynamical approach based on weak KAM(Kolmogorov-Arnold-Moser) theory due to Fathi. We establish a general convergence result for viscosity solutions and adherence of the graph as t →∞.展开更多
基金financially supported by National Natural Science Foundation of China(grant numbers:52171100,U20A20234)National Key R&D Program of China(grant number:2021YFB3701100)。
文摘The performance of Mg alloys is significantly influenced by the concentrations and solid solution behavior of the alloying elements.In this work,the solid solution behavior of 20 alloying elements in 190 ternary Mg alloy systems at 500℃are systematically investigated.The solid solution behavior of a set of two different alloying elements in Mg alloy systems are suggested to be classified into three categories:inclusivity,exclusivity and proportionality.Inclusivity classification indicates that the two alloying elements are inclusive inα-Mg,increasing the joint solubility of both elements.Exclusivity classification suggests that the two alloying elements have a low joint solid solubility inα-Mg,since they prefer to form stable second phases.For the proportionality classification,the solubility curve of the ternary Mg alloy systems is a straight line connecting the solubility points of the two sub-binary systems.The proposed classification theory was validated by key experiments and the calculation of formation energies.The interaction effects between alloying elements and the preference of formation of second phases are the main factors determining the solid solution behavior classifications.Based on the observed solid solution features of multi-component Mg alloys,principles for alloy design of different types of high-performance Mg alloys were proposed in this work.
基金the National Natural Science Foundation of China(Nos.91333103 and 21574053).
文摘Solvents have an essential association with polymer solution behavior.However,few researches have been deeply done on this respect.In recent years,our research group focus on the study on effect of solvent properties on solution behavior and film condensed state structure for semi-rigid conjugated polymer up till to apply for optoelectronic device.Herein,influence of solvent properties including solubility of solvent,aromaticity,polarity and hydrogen bonds on semi-rigid polymer chain solution behavior,i.e.,single chain conformation,chain shape,size and chains aggregated density were studied by means of static/dynamic laser light scattering(DLS/SLS)and exponential law etc.Effect of solvent properties on condensed state structure of the semi-rigid conjugated polymer film was studied by UV absorption spectroscopy,PL spectroscopy and electron microscopy etc.The essential reasons for the influence were discovered and the mechanism was revealed.It was found that solution behavior with different solvent properties had an essential physical relationship with chains condensed state structure of the semi-rigid conjugated polymers.More importantly,there was a quantitative structure-activity relationship between solution and film.The key to this relationship depended on the interaction between solvent molecules and the semi-rigid conjugated polymer chains.This interaction could also affect optoelectronic devices performance.This study is of great significance to effectively control the condensed state structure of the semirigid conjugated polymers in the process of dynamic evolution from solutions to films.It not only enriches the knowledge and understanding of both semi-rigid conjugated polymer solution behaviors and film condensed state physics based on polymer physics,but also is meaningful to practical application for conjugated polymer and other traditional polymer systems.
基金financially supported by the National Natural Science Foundation of China(Nos.91333103 and 21574053)。
文摘The solventnatures are crucial to deeply reveal solution behavior of macromolecular chains,physical essence of condensed state structures formation of the film as well as the photoelectronic devices performance.Based on the second virial coefficient(A2),effect of the synergistic action of solvents and external electric field on both solution behavior and the film’s condensed state structure for the semi-rigid conjugated polymer,poly[2-methoxy-5-(2’-ethylhexoxy)-1,4-phenylvinylene](MEH-PPV)was investigated by dynamic/static light scattering,photoluminescence spectroscopy and transmission electron microscopy,etc.It was found that although the MEH-PPV solutions with different solvents(toluene,chlorobenzene,chloroform and tetrahydrofuran)all could generate a response to the external electric field,the degree of response varied significantly with the change of solvent nature.Furthermore,ordered degree of the film from the solutions was also obviously different.The essential reason for this responsive difference was firstly revealed in the research,which actually depended on the degree of interaction between the solute and solvent,and this degree of interaction could be quantitatively described by the second virial coefficient(A2).The bigger the A2,the stronger the interaction between solvent and solute in the solution,and the stronger the response to the external electric field.Further,under the induction of external electric field,chains aggregations with different sizes were formed accompanied by large-scale chains ordered structure in the solution.This ordered structure not only can effectively transfer to film prepared by the precursor solution but also is beneficial to enhance the carrier mobility and device efficiency of the photoelectronic film.
文摘This paper deals with reaction-diffusion system with nonlocal source. It is proved that there exists a unique classical solution and the solution either exists globally or blows up in finite time. Furthermore, its blow-up set and asymptotic behavior are obtained provided that the solution blows up in finite time.
基金The authors gratefully a.cknowledge financial supportfrom th6 Natiol-al Natural Science Foundatiol- of CI-h-a. The number of
文摘Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.
文摘By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.
文摘A novel amphiphile of 4-[4-(4-decyloxyphenylazo) naphthyloxy] butyl trimethylammonium bromide has been synthesized. It can form the stable bilayer in dilute aqueous solution.
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
文摘The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions for [GRAPHICS] and for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the existence is reduced.
文摘Consider an initial-boundary problem vt - ux=0,u, + （）x + f（u） = （）x,θt+ux=（）ux=（）x+ （E） v（x,0） = v0（x）,u（x,0） = u0（x）,θ（0,x） = θ0（x）, （I） u（t,0） = u（t,1） = θx（t,0） = θx（t,1） （J） Sufficient and necessary conditions for （E）, （I） and （J） to have asymptotic stability of the gobal smooth solution are given by means of the elemental L2 energy method.
文摘A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained by Ladas, Sficas and Gopalsamy.
基金Supported by the National Natural Science Foundation of China under Grant No.11261037the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111+1 种基金the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
文摘We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particular, the double peakon solutions of both equations are investigated in detail. At the same time, the dynamic behaviors of three types double peakon solutions are analyzed by some figures.
基金Supported by the National Natural Science Foundation of China under Grant No.11261037the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111+1 种基金the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
文摘This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.
文摘In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,apriori evaluations for this function are obtained.Then,by imposing some conditions on the function on the right-hand side of the equation and using appropriate inequalities,it is shown that the solution is asymptotically damped.
文摘A controlled cross-linking polymerization containing intra- and intermolecular reactions was designed based on random coil morphology of macromolecules in solution. The soluble intramolecular cross-linked maeromolecule （ICM） was successfully synthesized in the system with PVA and MDI. We found an especial dissolving phenomenon, namely the semi-soluble phenomenon when some gels dissolved in DMF. The chain growth process of ICMs was investigated by Transmission electron microscopy （TEM） pictures of samples at different reacting times, in addition, TEM pictures show ICMs have three kinds of styles in structure, viz. ＂globule structure＂, ＂nubby structure＂ and the intervenient between the above two structures, and the efflux time of the ICMs was measured by an Ubbelohde viscosimeter, it was found that the efflux time decreases with the degree ofcrosslink increasing.
文摘This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1.
基金This work is supported by the National Natural Science Foundation of China （10471108）.
文摘This paper is concerned with the asymptotic behavior of solution to the following model involving two species all with chemotaxis：{αp/αt=Dp△（p△lnp/w）,αp/αt=Dq△（q△lnq/w）,αw/αt=βp-δw,p△ln（p/w）.^-n=q△ln（q/w）.^-n=0.We prove that the solution exists globally asβ ≥ 0. Asβ 〈 0, whether the solution exists globally or not depends on the initial data. By function transformation and compari- son, the asymptotical behavior of the solution is studied.
文摘In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the solutions to the equation are some high order of infinities,and also that some conditions which guarantee that every oscillatory solution to the equation has the property that the i order L operator of it tends to infinity when its independent variable tends to zero.
文摘IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M<sub>1</sub>, M<sub>2</sub> and M<sub>3</sub> which can react with each other to produce two new kinds of other chemical compounds: （M<sub>2</sub>）<sub>n</sub> （M<sub>1</sub>）<sub>m</sub> and （M<sub>3</sub>）<sub>r</sub> （M<sub>1</sub>）<sub>κ</sub> at the same time. Usually, these reactions are irreversible and they have the following forms:
基金supported by National Natural Science Foundation of China(Grant Nos.1132510311301106 and 11201288)+1 种基金China Postdoctoral Science Foundation(Grant No.2014M550210)Guangxi Experiment Center of Information Science(Grant No.YB1410)
文摘We study the long-time behavior of viscosity solutions for time-dependent Hamilton-Jacobi equations by the dynamical approach based on weak KAM(Kolmogorov-Arnold-Moser) theory due to Fathi. We establish a general convergence result for viscosity solutions and adherence of the graph as t →∞.
