Reaction–diffusion problem with an obstacle potential

doi:10.1088/0951-7715/22/11/008

Finite-dimensional global and exponential attractors for the reaction–diffusion problem with an obstacle potential

Antonio Segatti et al 2009 Nonlinearity 22 2733-2760 doi: 10.1088/0951-7715/22/11/008

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Antonio Segatti¹ and Sergey Zelik²
¹ Dipartimento di Matematica 'F.Casorati', Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy
² Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK
E-mail: antonio.segatti@unipv.it and s.zelik@surrey.ac.uk

Recommended by C-Q Cheng

Abstract. A reaction–diffusion problem with an obstacle potential is considered in a bounded domain of $\mathbb R^N$ . Under the assumption that the obstacle $\mathscr{K}$ is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed n-dimensional simplex, we prove that the long-time behaviour of the solution semigroup associated with this problem can be described in terms of an exponential attractor. In particular, the latter means that the fractal dimension of the associated global attractor is also finite.

Mathematics Subject Classification: 37L30, 35B41, 35K57

Print publication: Issue 11 (November 2009)
Received 16 February 2009, in final form 17 September 2009
Published 13 October 2009

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Finite-dimensional global and exponential attractors for the reaction–diffusion problem with an obstacle potential

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