DYNAMICS OF A REACTION–DIFFUSION EQUATION WITH A DISCONTINUOUS NONLINEARITY-Reference-Cited by-同舟云学术

DYNAMICS OF A REACTION–DIFFUSION EQUATION WITH A DISCONTINUOUS NONLINEARITY

Published:2006-10 Issue:10 Volume:16 Page:2965-2984
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

ARRIETA JOSÉ M.¹,RODRÍGUEZ-BERNAL ANÍBAL¹,VALERO JOSÉ²

Affiliation:

1. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain

2. Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. de la Universidad s/n, 03202 Elche (Alicante), Spain

Abstract

We study the nonlinear dynamics of a reaction–diffusion equation where the nonlinearity presents a discontinuity. We prove the upper semicontinuity of solutions and the global attractor with respect to smooth approximations of the nonlinear term. We also give a complete description of the set of fixed points and study their stability. Finally, we analyze the existence of heteroclinic connections between the fixed points, obtaining information on the fine structure of the global attractor.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127406016586

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