Existence of pullback attractors for pullback asymptotically compact processes

By Tomás Caraballo, Alexandre Nolasco de Carvalho, José A. Langa, Felipe Rivero. 2010

84 citations recorded by the source corpus.

Abstract This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results that extend the following results for autonomous evolution processes (semigroups) (i) An autonomous evolution process which is bounded, dissipative and asymptotically compact has a global attractor. (ii) An autonomous evolution process which is bounded, point dissipative and asymptotically compact has a global attractor. The extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and non-autonomous evolution processes. An application to damped wave problem with non-autonomous damping is considered.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/226b808df77888a761409f72b3bab71a7a619d1a

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In Computational Theory and Mathematics

In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

Pullback exponential attractors for nonautonomous equations Part I: Semilinear parabolic problems (2011, background): “1] (see also [1] for the discussion on the existence of pullback global attractors).”
Pullback exponential attractors for evolution processes in Banach spaces: Theoretical results (2013, background): “[1]), and the finite dimensionality of global pullback attractors that are not uniformly bounded in the past has been an open problem (see [11] or Remark 3.”
Pullback exponential attractors for evolution processes in Banach spaces: Properties and applications (2013, background): “For the proof of the following lemma we refer to [3].”