WIAS Preprint No. 505, (1999)

The attractor for a nonlinear reaction-diffusion system in an unbounded domain



Authors

  • Efendiev, Messoud
  • Zelik, Sergey

2010 Mathematics Subject Classification

  • 35B40 35B45

Keywords

  • Reaction-diffusion systems, unbounded domains, global attractor, trajectory attractor, Hausdorff and fractal dimension

Abstract

In this paper the quasilinear second order parabolic systems of reaction-diffusion type in an unbounded domain are considered. Our aim in this article is to study the long-time behaviour of parabolic systems for which the nonlinearity depends explicitely on the gradient of the unknown functions. To this end we give a systematic study of given parabolic systems and their attractors in weighted Sobolev spaces. Dependence of the Hausdorff dimension of attractors from weight of the Sobolev spaces are considered.

Appeared in

  • Comm. Pure Appl. Math. 54 (2001), no. 6, 625--688

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