A class of doubly degenerate parabolic        equations with periodic sources

Jiebao Sun; Boying Wu; Jing Li; Dazhi Zhang

doi:10.3934/dcdsb.2010.14.1199

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2010, Volume 14, Issue 3: 1199-1210. Doi: 10.3934/dcdsb.2010.14.1199

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A class of doubly degenerate parabolic equations with periodic sources

1.
Department of Mathematics, Harbin Institute of Technology, Harbin 150001

Received: April 30, 2009

Revised: February 28, 2010

Published: September 2010

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Abstract

In this paper, we investigate a class of doubly degenerate parabolic equations with periodic sources subject to homogeneous Dirichlet boundary conditions. By means of the theory of Leray-Schauder degree, we establish the existence of non-trivial nonnegative periodic solutions. The key step is how to establish the uniform bound estimate of approximate solutions, for this purpose we will make use of Moser iteration and some results of the eigenvalue problem for the $p$-Laplacian equation.

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Mathematics Subject Classification: 35K57, 35K65, 35B10.

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