Periodic solutions of a non-divergent diffusion equation with nonlinear sources

Chunhua Jin; Jingxue Yin

doi:10.3934/dcdsb.2012.17.101

Article Contents

2012, Volume 17, Issue 1: 101-126. Doi: 10.3934/dcdsb.2012.17.101

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Periodic solutions of a non-divergent diffusion equation with nonlinear sources

Chunhua Jin^1, and
Jingxue Yin^2,

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024
2.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631

Received: June 30, 2010

Revised: February 28, 2011

Published: December 2011

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Abstract

This paper is concerned with the existence of nontrivial and nonnegative periodic solutions of a doubly degenerate and singular parabolic equation in non-divergent form with nonlinear sources. We will determine exact classification for the exponent values of the source, and so, for the nonexistence of nontrivial periodic solutions, as well as the existence of those solutions with compact support, and the existence of positive periodic solutions.

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

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