Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forw...Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.展开更多
In this paper, we prove the existence of the pullback attractor for the nonautonomous Benjamin-Bona-Mahony equations in H2 by establishing the pullback uniformly asymptotical compactness.
A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynam- ical system. It is shown that the compact equi-att...A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynam- ical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.展开更多
The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to pr...The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes eauations is given.展开更多
The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence...The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.展开更多
In this paper, we consider a non-autonomous model for epitaxial growth. It is shown that a pullback attractor of the model exists when the external force has exponential growth.
1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of ...1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.展开更多
The existence of pullback attractors for semi-uniformly dissipative dynamical systems under some asymptotic compactness assumptions is considered.A sufficient condition for the existence of pullback attractors is pres...The existence of pullback attractors for semi-uniformly dissipative dynamical systems under some asymptotic compactness assumptions is considered.A sufficient condition for the existence of pullback attractors is presented.Then,the results are applied to non-autonomous 2D Navier-Stokes equations.展开更多
In this paper, we study the global and pullback attractors for a strongly damped wave equation with delays when the force term belongs to different space. The results following from the solution generate a compact set.
This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we...This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we establish the existence of pullback attractors for the fluid flow model,which is dependent on the past state.Inspired by the idea in Zelati and Gal’s paper(JMFM,2015),the robustness of pullback attractors has been proved via upper semi-continuity in last section.展开更多
In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g（t, ut） may be driven by a function with very weak assumptions, ...In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g（t, ut） may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback ：D-attractor in CH01（Ω） × CL2 （Ω） by constructing the energy functional and combining with the idea of the contractive function.展开更多
This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated proces...This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.展开更多
The existence of a pullback attractor is proven for the non-autonomous Benjamin-Bona-Mahony equation in unbounded domains.The asymptotic compactness of the solution operator is obtained by the uniform estimates on the...The existence of a pullback attractor is proven for the non-autonomous Benjamin-Bona-Mahony equation in unbounded domains.The asymptotic compactness of the solution operator is obtained by the uniform estimates on the tails of solutions.展开更多
This paper is concerned with the existence of pullback attractors for the three dimensional nonautonomous Navier-Stokes-Voight equations for the processes generated by the weak and strong solutions. The main difficult...This paper is concerned with the existence of pullback attractors for the three dimensional nonautonomous Navier-Stokes-Voight equations for the processes generated by the weak and strong solutions. The main difficulty is how to establish the pullback asymptotic compactness via energy equation approach under suitable assumption on external force.展开更多
Under the assumption that ?g(t) is translation bounded in , and using the method developed in [3], we prove the existence of pullback exponential attractors in ?for nonlinear reaction diffusion equation with polynomia...Under the assumption that ?g(t) is translation bounded in , and using the method developed in [3], we prove the existence of pullback exponential attractors in ?for nonlinear reaction diffusion equation with polynomial growth nonlinearity(?is arbitrary).展开更多
基金supported by China Postdoctoral Science Foundation (2020TQ0053 and 2020M680456)the research funds of Qianshixinmiao[2022]B16,Qianjiaoji[2022]124 and Qiankehepingtairencai-YSZ[2022]022+1 种基金supported by the NSFC (11731014 and 11571254)supported by the NSFC (11971067,11631008,11771183)。
文摘Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.
基金supported by the NSF of China(11031003, 10871040)
文摘In this paper, we prove the existence of the pullback attractor for the nonautonomous Benjamin-Bona-Mahony equations in H2 by establishing the pullback uniformly asymptotical compactness.
基金supported by the National Natural Science Foundation of China(11571283)supported by Natural Science Foundation of Guizhou Province
文摘A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynam- ical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.
基金Project supported by the National Natural Science Foundation of China (No. 10871156)the Fund of Xi’an Jiaotong University (No. 2009xjtujc30)
文摘The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes eauations is given.
基金supported by the National Natural Science Foundation of China (No.10871156)the Fund of Xi'an Jiaotong University (No.2009xjtujc30)
文摘The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.
基金The NSF(11401258)of Chinathe NSF(BK20140130)of Jiangsu Province
文摘In this paper, we consider a non-autonomous model for epitaxial growth. It is shown that a pullback attractor of the model exists when the external force has exponential growth.
文摘1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.
基金National Natural Science Foundations of China(No.70773075,No.10871040)Chinese Universities Scientific Fund(No.10D10911)+1 种基金State key Program of National Science of China(No.11031003)Mathematical Tianyuan Foundation of China(No.11026136)
文摘The existence of pullback attractors for semi-uniformly dissipative dynamical systems under some asymptotic compactness assumptions is considered.A sufficient condition for the existence of pullback attractors is presented.Then,the results are applied to non-autonomous 2D Navier-Stokes equations.
文摘In this paper, we study the global and pullback attractors for a strongly damped wave equation with delays when the force term belongs to different space. The results following from the solution generate a compact set.
基金Xin-Guang Yang was partially supported by the Fund of Young Backbone Teacher in Henan Province(No.2018GGJS039)cultivation Fund of Henan Normal University(No.2020PL17)Henan Overseas Expertise Introduction Center for Discipline Innovation(No.CXJD2020003).
文摘This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we establish the existence of pullback attractors for the fluid flow model,which is dependent on the past state.Inspired by the idea in Zelati and Gal’s paper(JMFM,2015),the robustness of pullback attractors has been proved via upper semi-continuity in last section.
基金Supported by the NSFC(Grants Nos.11471148 and 11601522)the Fundamental Research Funds for the Central Universities of China(Grant No.17CX02036A)the Provincial Natural Science Foundation of Hu’nan(Grant No.2017JJ3222)
文摘In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g（t, ut） may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback ：D-attractor in CH01（Ω） × CL2 （Ω） by constructing the energy functional and combining with the idea of the contractive function.
基金partially supported by the Natural Science Foundation of China(11671134)
文摘This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.
文摘The existence of a pullback attractor is proven for the non-autonomous Benjamin-Bona-Mahony equation in unbounded domains.The asymptotic compactness of the solution operator is obtained by the uniform estimates on the tails of solutions.
基金in part supported by the NNSF of China(No.10871040,11671075)supported in part by Ph.D.Innovative Fund of Donghua University(No.104-06-0019089)+2 种基金the Fund of Young Backbone Teacher in Henan Province(No.2018GGJS039)the Key Project of Science and Technology of Henan Province(Grant No.182102410069)supported by the National Natural Science Foundation of China(No.11801357)
文摘This paper is concerned with the existence of pullback attractors for the three dimensional nonautonomous Navier-Stokes-Voight equations for the processes generated by the weak and strong solutions. The main difficulty is how to establish the pullback asymptotic compactness via energy equation approach under suitable assumption on external force.
文摘Under the assumption that ?g(t) is translation bounded in , and using the method developed in [3], we prove the existence of pullback exponential attractors in ?for nonlinear reaction diffusion equation with polynomial growth nonlinearity(?is arbitrary).
