In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets ...In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets and global attractor.展开更多
In this paper, the global existence of classical solution and global attractor for Camassa-Holm type equations with dissipative term are established by using fixed point theorem and a priori estimates.
In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded doma...In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k（Ω） in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k ∈ [0, 1] to the case k∈ [0, ∞）.展开更多
This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with t...This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.展开更多
A class of strongly damped nonlinear wave equations are studied by using the technique of the operator decomposition,and the existence of the global compact attractor in space D(A)×V is obtained.
In this paper, a chemotaxis model with reproduction term in a bounded domain Ω R^n is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.
This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals t...This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals that the solutions lying in the global attractor are analytic in time with values in a Gevrey class of analytic functions in space.展开更多
In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semi...In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global展开更多
The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved i...The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .展开更多
The existences of the global attractor Ae for a degenerate parabolic equation and of the homogenized attractor A0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between...The existences of the global attractor Ae for a degenerate parabolic equation and of the homogenized attractor A0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between Ae and A0 are given.展开更多
In this paper,we consider the initial-boundary problem for Zakharov equations arising from ion-acoustic modes and obtain the existence of global attractor for the initialboundary problem for Zakharov equations.
This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the cor...This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.展开更多
Using a new method developed in [5], we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H^3per（Ω） and H^4per（Ω）.
In this paper,We study the global attractor and its properties on in nite lattice dynamical system FitzHugh-Nagumo in a weighted space lσ^2×lσ^2.We prove the existence and uniqueness of the solution to the latt...In this paper,We study the global attractor and its properties on in nite lattice dynamical system FitzHugh-Nagumo in a weighted space lσ^2×lσ^2.We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in lσ^2×lσ^2.Then we get a bounded absorbing set,which suggests the existence of global attractors.Finally,we study the uniform boundedness and the upper semicontinuity of the global attractor.展开更多
In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the se...In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets.展开更多
In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Mira...In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7, 8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.展开更多
A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference sche...A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L^2 × H^1 × H^2 over a finite time interval （0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.展开更多
This paper is concerned with the following nonlinear difference equation:x_(n+1)=sum from i=1 to l A_(s_i)x_(n-s_i)/B+C multiply from j=1 to k x_(n-t_j) +D_x_n,n=0,1,…(1.1).The more simple suffcient conditions of asy...This paper is concerned with the following nonlinear difference equation:x_(n+1)=sum from i=1 to l A_(s_i)x_(n-s_i)/B+C multiply from j=1 to k x_(n-t_j) +D_x_n,n=0,1,…(1.1).The more simple suffcient conditions of asymptotic stability are obtained by using a smart technique,which extends and includes partially corresponding results obtained in the references [6-9].The global behavior of the solutions is investigated.In addition,in order to support analytic results,some numerical simulations to the special equations are presented.展开更多
This paper corrects some mistakes in the proof of absorbing sets theorem of at-tractors of non-Newtonian fluids, and establishes again the existence of bounded absorbing sets.
文摘In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets and global attractor.
文摘In this paper, the global existence of classical solution and global attractor for Camassa-Holm type equations with dissipative term are established by using fixed point theorem and a priori estimates.
文摘In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k（Ω） in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k ∈ [0, 1] to the case k∈ [0, ∞）.
基金partially supported by NNSF of China(11571126,11701198)China Postdoctoral Science Foundation funded project(2017M622397)
文摘This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.
文摘A class of strongly damped nonlinear wave equations are studied by using the technique of the operator decomposition,and the existence of the global compact attractor in space D(A)×V is obtained.
基金Supported by National Natural Science Foundation of China (10871151)
文摘In this paper, a chemotaxis model with reproduction term in a bounded domain Ω R^n is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.
基金Supported by NSF of China(11971356)NSF of Zhejiang Province(LY17A010011)。
文摘This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals that the solutions lying in the global attractor are analytic in time with values in a Gevrey class of analytic functions in space.
基金Supported by the NNSF of China(11031003,11271066)Supported by the Shanghai Education Commission(13ZZ048)
文摘In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global
文摘The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .
基金the Scientific Research Foundation for Returned Overseas Chinese Scholars under the State Education Ministrythe Key Teachers’Foundation of Chongqing University
文摘The existences of the global attractor Ae for a degenerate parabolic equation and of the homogenized attractor A0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between Ae and A0 are given.
基金Supported by the National Natural Science Foundation of China（10871075） Supported by the Natural Science Foundation of Guangdong Province（9151064201000040 9451027501002564）
文摘In this paper,we consider the initial-boundary problem for Zakharov equations arising from ion-acoustic modes and obtain the existence of global attractor for the initialboundary problem for Zakharov equations.
基金Supported by Natural Science Foundation of China(1077107410771139)+1 种基金Supported by the NSF of Wenzhou University(2007L024)Supported by the NSF of Zhejiang Province(Y6080077)
文摘This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.
基金the NNSF of China(107711597)the NNSF of Gansu(3ZS041A25-006)
文摘Using a new method developed in [5], we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H^3per（Ω） and H^4per（Ω）.
基金Supported by The Scientic Research Foundation Funded by Hunan Provincial Education Department under grant 19A503Partially supported by Hunan Provincial Exploration of Undergraduate Research Learning and Innovative Experiment Project:2018XTUSJ008Hunan Provincial Natural Science Foundation of China under grant 2015JJ2144.
文摘In this paper,We study the global attractor and its properties on in nite lattice dynamical system FitzHugh-Nagumo in a weighted space lσ^2×lσ^2.We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in lσ^2×lσ^2.Then we get a bounded absorbing set,which suggests the existence of global attractors.Finally,we study the uniform boundedness and the upper semicontinuity of the global attractor.
基金Supported by the National Natural Science Foundation of China（l1671075）
文摘In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets.
基金supported by NSFC Grant (11031003)the Fundamental Research Funds for the Central Universities+1 种基金support by Fund of excellent young teachers in Shanghai (shgcjs008)Initial Fund of SUES (A-0501-11-016)
文摘In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7, 8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.
基金Supported by the National Natural Science Foundation of China(10371077)
文摘A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L^2 × H^1 × H^2 over a finite time interval （0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.
基金Supported by the Science and Technology Project of Chongqing Municiple Education Commission(KJ110501)Supported by the Research Initiation Project for High-level Talents of North China University of Water Resources and Electric Power(201035)Supported by the NSF of the Hebei Higher Education Institutions(Z2011111)
文摘This paper is concerned with the following nonlinear difference equation:x_(n+1)=sum from i=1 to l A_(s_i)x_(n-s_i)/B+C multiply from j=1 to k x_(n-t_j) +D_x_n,n=0,1,…(1.1).The more simple suffcient conditions of asymptotic stability are obtained by using a smart technique,which extends and includes partially corresponding results obtained in the references [6-9].The global behavior of the solutions is investigated.In addition,in order to support analytic results,some numerical simulations to the special equations are presented.
文摘This paper corrects some mistakes in the proof of absorbing sets theorem of at-tractors of non-Newtonian fluids, and establishes again the existence of bounded absorbing sets.
