Trajectory and global attractors for evolution equations with memory

Our aim in this note is to analyze the relation between two notions of attractors for the study of the long time behavior of equations with memory, namely, the global attractor in the so-called past history approach, and the more recently proposed notion of trajectory attractor.

[1]  V. Chepyzhov,et al.  Attractors for Equations of Mathematical Physics , 2001 .

[2]  I. Chueshov,et al.  Long—time behaviour of strong solutions of retarded nonlinear P.D.E.s , 1997 .

[3]  Alain Miranville,et al.  Trajectory and global attractors of dissipative hyperbolic equations with memory , 2004 .

[4]  Vittorino Pata,et al.  Singular limit of differential systems with memory , 2006 .

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

[6]  Vittorino Pata,et al.  SINGULAR LIMIT OF DISSIPATIVE HYPERBOLIC EQUATIONS WITH MEMORY , 2005 .

[7]  Peter E. Kloeden,et al.  PULLBACK AND FORWARD ATTRACTORS FOR A DAMPED WAVE EQUATION WITH DELAYS , 2004 .

[8]  Uniform attractors for a non-autonomous semilinear heat equation with memory , 2000 .

[9]  Vittorino Pata,et al.  Asymptotic behavior of a semilinear problem in heat conduction with memory , 1998 .

[10]  Vladimir V. Chepyzhov,et al.  On Trajectory and Global Attractors for Semilinear Heat Equations with Fading Memory , 2006 .

[11]  A. Rezounenko.  Approximate Inertial Manifolds for Retarded Semilinear Parabolic Equations , 2002 .

[12]  I. Chueshov,et al.  Global attractors for a class of retarded quasilinear partial differential equations , 1995 .

[13]  C. Dafermos.  Asymptotic stability in viscoelasticity , 1970 .

[14]  Vittorino Pata,et al.  Attractors for a damped hyperbolic equation with linear memory , 2001 .

[15]  V. Chepyzhov,et al.  Evolution equations and their trajectory attractors , 1997 .