Long-time dynamics of the parabolic $p$-Laplacian equation

Pelin G. Geredeli; Azer Khanmamedov

doi:10.3934/cpaa.2013.12.735

Article Contents

2013, Volume 12, Issue 2: 735-754. Doi: 10.3934/cpaa.2013.12.735

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Long-time dynamics of the parabolic $p$-Laplacian equation

Pelin G. Geredeli^1, and
Azer Khanmamedov^1,

1.
Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06800, Ankara

Received: June 30, 2011

Revised: February 29, 2012

Published: February 2013

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Abstract

In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under the mild conditions on the coefficient of the principal part and without upper growth restriction on the source function, we prove that this problem possesses a compact and invariant global attractor in $L^2(R^n)$.

Keywords:

$p$-Laplacian equation,
attractors.

Mathematics Subject Classification: 35L55, 35B41.

Citation:

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