This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of e...This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.展开更多
The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov en...The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.展开更多
This paper is concerned with the three-dimensional non-autonomous Brinkman- Forchheimer equation. By Galerkin approximation method, we give the existence and uniqueness of weak solutions for non-autonomous Brinkman-Fo...This paper is concerned with the three-dimensional non-autonomous Brinkman- Forchheimer equation. By Galerkin approximation method, we give the existence and uniqueness of weak solutions for non-autonomous Brinkman-Forchheimer equation. And we investigate the asymptotic behavior of the weak solution, the existence and structures of the （H, H）-uniform attractor and （H, V）-uniform attractor. Then we prove that an L2-uniform attractor is actually an HI-uniform 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 paper, a third order（in time） partial differential equation in R^n is con-sidered. By using semigroup method and constructing Lyapunov function, we establish the global existence, asymptotic behavior and uni...In this paper, a third order（in time） partial differential equation in R^n is con-sidered. By using semigroup method and constructing Lyapunov function, we establish the global existence, asymptotic behavior and uniform attractors in nonhomogeneous case. In addition, we also obtain the results of well-uosedness in semilinear case.展开更多
In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the...In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the method of uniform contractive functions. We finally investigate an alternative result of solutions for the semilinear thermoelastic systems by virtue of the semigroup method.展开更多
In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timosh...In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method.展开更多
In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdor...In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdorff dimension of the uniform attractor.展开更多
This paper considers the existence of uniform attractors for a non-autonomous thermoviscoelastic equation with strong damping in a bounded domain Ω⊆Rn(n≥1) by establishing the uniformly asymptotic compactn...This paper considers the existence of uniform attractors for a non-autonomous thermoviscoelastic equation with strong damping in a bounded domain Ω⊆Rn(n≥1) by establishing the uniformly asymptotic compactness of the semi-process generated by the global solutions.展开更多
In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a no...In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.展开更多
In this paper, we prove the existence of a uniform attractor for non-autonomous Brinkman-Forchheimer equations with general delay and time-dependent external force.
In this paper we show the existence of the uniform attractors for the family of processes corresponding to the suspension bridge equations in H02 × L2 by a new concept of Condition （C＊） and the enegy estimats ...In this paper we show the existence of the uniform attractors for the family of processes corresponding to the suspension bridge equations in H02 × L2 by a new concept of Condition （C＊） and the enegy estimats methods.展开更多
This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajector...This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.展开更多
In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the...In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the process in the phase apace. In a certain parameter region, the exponential attractor is a uniformly exponentially attracting time-dependent set in the phase apace, and is finite-dimensional no matter how complex the dependence of the external forces on time is. On this basis, we also obtain the existence of the infinite-dimensional uniform exponential attractor for the system.展开更多
The long-time behaviour of a two-dimensional nonautonomous nonlinear Schrodinger equation is considered. The existence! of uniform attractor is proved and the upper bound of the uniform attractor's Housdorff dimen...The long-time behaviour of a two-dimensional nonautonomous nonlinear Schrodinger equation is considered. The existence! of uniform attractor is proved and the upper bound of the uniform attractor's Housdorff dimension is given.展开更多
In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equ...In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equation.estimate of fractal dimension of attractor.展开更多
基金Sponsored by the NSFC (10901121,10826091 and 10771139)NSF for Postdoctors of China (20090460952)+2 种基金NSF of Zhejiang Province (Y6080077)NSF of Wenzhou University (2008YYLQ01)by the Zhejiang Youth Teacher Training Project and Wenzhou 551 Project
文摘This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.
基金Project supported by the National Natural Science Foundation of China(No.10771139)the Ph.D. Program of Ministry of Education of China(No.200802700002)+4 种基金the Shanghai Leading Academic Discipline Project(No.S30405)the Innovation Program of Shanghai Municipal Education Commission(No.08ZZ70)the Foundation of Shanghai Talented Persons(No.049)the Leading Academic Discipline Project of Shanghai Normal University(No.DZL707)the Foundation of Shanghai Normal University(No.DYL200803)
文摘The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.
基金Supported by the National Natural Science Foundation of China (Grants No. 10871156)
文摘This paper is concerned with the three-dimensional non-autonomous Brinkman- Forchheimer equation. By Galerkin approximation method, we give the existence and uniqueness of weak solutions for non-autonomous Brinkman-Forchheimer equation. And we investigate the asymptotic behavior of the weak solution, the existence and structures of the （H, H）-uniform attractor and （H, V）-uniform attractor. Then we prove that an L2-uniform attractor is actually an HI-uniform 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 the National Natural Science Foundation of China(11271066)Supported by the Shanghai Education Commission(13ZZ048)
文摘In this paper, a third order（in time） partial differential equation in R^n is con-sidered. By using semigroup method and constructing Lyapunov function, we establish the global existence, asymptotic behavior and uniform attractors in nonhomogeneous case. In addition, we also obtain the results of well-uosedness in semilinear case.
文摘In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the method of uniform contractive functions. We finally investigate an alternative result of solutions for the semilinear thermoelastic systems by virtue of the semigroup method.
基金Supported by the National Natural Science Foundation of China(11271066)Supported by the Shanghai Education Commission(13ZZ048)
文摘In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method.
基金The NSF(10771139)of ChinaSpecial Fund(gjd-07011)of Scientific Research for Shang-hai's Excellent Young College TeachersKey Subjects(xk0704)on Management Science and Engineering.
文摘In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdorff dimension of the uniform attractor.
文摘This paper considers the existence of uniform attractors for a non-autonomous thermoviscoelastic equation with strong damping in a bounded domain Ω⊆Rn(n≥1) by establishing the uniformly asymptotic compactness of the semi-process generated by the global solutions.
基金Supported by the National Natural Science Foundation of China(No.1127106611671075)a grant from Shanghai Municipal Eduction Commission(No.13ZZ048)
文摘In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.
基金Supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education,Science and Technology(Grant No.2012R1A1A3011630)
文摘In this paper, we prove the existence of a uniform attractor for non-autonomous Brinkman-Forchheimer equations with general delay and time-dependent external force.
基金Supported by the National Natural Science Foundation of China (Grant No.10671158)the Education Department Foundation of Gansu Province (Grant No.0801-02)+1 种基金the Natural Sciences Foundation of Gansu Province (Grant No.3ZS061-A25-016)NWNU-KJCXGC-03-40
文摘In this paper we show the existence of the uniform attractors for the family of processes corresponding to the suspension bridge equations in H02 × L2 by a new concept of Condition （C＊） and the enegy estimats methods.
基金Supported by NSFC(51209242,2011BAB09B01,11271290)NSF of Zhejiang Province(LY17A010011)
文摘This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.
文摘In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the process in the phase apace. In a certain parameter region, the exponential attractor is a uniformly exponentially attracting time-dependent set in the phase apace, and is finite-dimensional no matter how complex the dependence of the external forces on time is. On this basis, we also obtain the existence of the infinite-dimensional uniform exponential attractor for the system.
文摘The long-time behaviour of a two-dimensional nonautonomous nonlinear Schrodinger equation is considered. The existence! of uniform attractor is proved and the upper bound of the uniform attractor's Housdorff dimension is given.
文摘In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equation.estimate of fractal dimension of attractor.
