Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction-diffusion equations

Abstract In this paper, we introduce the concept of norm-to-weak continuous process in a Banach space, and obtain the existence of pullback attractors for this kind of process. Then we give a new method for proving the existence of the pullback attractors. As an application, we obtain the existence of pullback attractors for nonautonomous reaction–diffusion equation in H 0 1 with exponential growth of the external force.

[1]  Peter E. Kloeden,et al.  The perturbation of attractors of skew-product flows with a shadowing driving system , 2001 .

[2]  Yejuan Wang,et al.  Pullback attractors of nonautonomous dynamical systems , 2006 .

[3]  J. Hale.  Asymptotic Behavior of Dissipative Systems , 1988 .

[4]  K. Deimling.  Nonlinear functional analysis , 1985 .

[5]  David Cheban,et al.  Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems , 2005 .

[6]  S. Siegmund,et al.  Pullback Attracting Inertial Manifolds for Nonautonomous Dynamical Systems , 2002 .

[7]  Hongqing Wu,et al.  Pullback attractors of nonautonomous reaction–diffusion equations , 2007 .

[8]  James C. Robinson.  Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors , 2001 .

[9]  Tomás Caraballo,et al.  Pullback attractors for asymptotically compact non-autonomous dynamical systems , 2006 .

[10]  Chengkui Zhong,et al.  The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction–diffusion equations☆ , 2006 .

[11]  Peter E. Kloeden,et al.  Nonautonomous systems, cocycle attractors and variable time-step discretization , 2004, Numerical Algorithms.

[12]  Hongqing Wu,et al.  Attractors for nonautonomous 2D Navier-Stokes equations with normal external forces , 2005 .

[13]  Peter E. Kloeden,et al.  Pullback Attractors in Dissipative Nonautonomous Differential Equations Under Discretization , 2001 .

[14]  R. Temam.  Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .

[15]  Peter E. Kloeden,et al.  On the asymptotical behavior of nonautonomous dynamical systems , 2004 .

[16]  D. Cheban,et al.  Global Attractors Of Non-autonomous Dissipative Dynamical Systems , 2004 .

[17]  Jinqiao Duan,et al.  Almost Periodic Solutions and Global Attractors of Non-autonomous Navier–Stokes Equations , 2004 .

[18]  Tomás Caraballo,et al.  Attractors for 2D-Navier–Stokes models with delays☆ , 2004 .

[19]  G. Sell,et al.  Dynamics of Evolutionary Equations , 2002 .

[20]  P. E. Kloeden,et al.  Global and pullback attractors of set-valued skew product flows , 2006 .

[21]  Chengkui Zhong,et al.  Necessary and sufficient conditions for the existence of global attractors for semigroups and applications , 2002 .