Existence of chaos in weakly quasilinear systems

Y. Charles Li

doi:10.3934/cpaa.2011.10.1331

Article Contents

2011, Volume 10, Issue 5: 1331-1344. Doi: 10.3934/cpaa.2011.10.1331

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Existence of chaos in weakly quasilinear systems

Y. Charles Li^1,

1.
Department of Mathematics, University of Missouri, Columbia, MO 65203

Received: January 31, 2009

Revised: July 31, 2010

Published: August 2011

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Abstract

The aim of this article is twofold: (1). develop a strategy to prove the existence of chaos in weakly quasilinear systems, (2). strengthen the existing results on chaos in partial differential equations. First, we study a sine-Gordon equation containing weakly quasilinear terms, and existence of chaos is proved. Then, we study a Ginzburg-Landau equation containing weakly quasilinear terms, and existence of chaos is proved under generic conditions. Finally, in the Appendix, we prove the existence of chaos in a reaction-diffusion equation.

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Mathematics Subject Classification: Primary 35, 37; Secondary 34, 46.

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