JournalsaihpcVol. 28, No. 4pp. 565–582

Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium

  • Messoud A. Efendiev

    Helmholtz Center Munich, Institute of Biomathematics and Biostatistics, Ingolstädter, Landstrasse 1, 85764 Neuherberg, Germany

  • Mitsuharu Ôtani

    Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium cover
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Abstract

In this paper we give a detailed study of the global attractors for parabolic equations governed by the p-Laplacian in a heterogeneous medium. Not only the existence but also the infinite dimensionality of the global attractors is presented by showing that their ε-Kolmogorov entropy behaves as a polynomial of the variable as ε tends to zero, which is not observed for non-degenerate parabolic equations. The upper and lower bounds for the Kolmogorov ε-entropy of infinite-dimensional attractors are also obtained.

Cite this article

Messoud A. Efendiev, Mitsuharu Ôtani, Infinite-dimensional attractors for parabolic equations with p-Laplacian in heterogeneous medium. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 4, pp. 565–582

DOI 10.1016/J.ANIHPC.2011.03.006