Article Contents

2014, Volume 34, Issue 10: 4155-4182. Doi: 10.3934/dcds.2014.34.4155

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Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term

1.
Kyiv National Taras Shevchenko University, 01033-Kyiv
2.
Institute for Applied System Analysis, National Technical University of Ukraine "KPI", Kyiv
3.
Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche

Received: September 2012

Revised: January 2013

Published: October 2014

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we study the structure of the global attractor for a reaction-diffusion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable manifold of the set of stationary points or the stable one but considering in this last case only solutions in the set of bounded complete trajectories.

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Mathematics Subject Classification: 35B40, 35B41, 35K55, 37B25, 58C06.

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