Global attractors for doubly nonlinear evolution equations with non-monotone perturbations

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7 Citations (Scopus)

Abstract

This paper addresses the analysis of dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to construct global attractors, an approach based on the notion of generalized semiflow is employed instead of the usual semigroup approach, since solutions of the Cauchy problem for the equation might not be unique. Moreover, the preceding abstract theory is applied to a generalized Allen-Cahn equation as well as a semilinear parabolic equation with a nonlinear term involving gradients.

Original languageEnglish
Pages (from-to)1850-1875
Number of pages26
JournalJournal of Differential Equations
Volume250
Issue number4
DOIs
Publication statusPublished - 2011 Feb 15
Externally publishedYes

Keywords

  • Doubly nonlinear evolution equation
  • Generalized Allen-Cahn equation
  • Generalized semiflow
  • Global attractor
  • Reflexive Banach space

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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