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
In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is ...In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.展开更多
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,th...The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.展开更多
A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the a...A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged i divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.展开更多
Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed.The existence and uniqueness of invariant measures are e...Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed.The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises.Some further developments,problems,and challenges in this direction are also discussed.展开更多
In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate....In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate.Utilizing energy methods,we show that under time-dependent Dirichlet boundary conditions,long-time dynamics of solutions are driven by their boundary data,and there is no restriction on the magnitude of initial energy.Moreover,the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions,which has not been observed in previous studies on related models.展开更多
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In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.
基金Project supported by the National Natural Science Foundation of China(Nos.10631020,10401019)the Basic Research Grant of Tsinghua University.
文摘The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
基金the Fundamental Research Funds for the Central Universities(Grants B200203009 and B200202126)the Natural Science Foundation of Jiangsu Province(Grant BK20190073)+2 种基金the State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant SKLA202001)the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University(Grant KF2020-22)the China Postdoctoral Science Foundation(Grants 2017M611669 and 2018T110430).
文摘A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged i divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.
基金supported by the UK Engineering and Physical Sciences Research Council Award EP/E035027/1,EP/L015811/1the Royal Society-Wolfson Research Merit Award(UK)an Oxford Croucher Scholarship
文摘Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed.The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises.Some further developments,problems,and challenges in this direction are also discussed.
基金partially supported by China Scholarship Council(No.201906150159)partially supported by China Scholarship Council(No.201906150101)+2 种基金National Natural Science Foundation of China(No.11971176,No.11871226)partially supported by Fundamental Research Funds for the Central Universities of China(No.3072020CFT2402)partially supported by Simons Foundation Collaboration Grant for Mathematicians(No.413028)。
文摘In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate.Utilizing energy methods,we show that under time-dependent Dirichlet boundary conditions,long-time dynamics of solutions are driven by their boundary data,and there is no restriction on the magnitude of initial energy.Moreover,the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions,which has not been observed in previous studies on related models.
