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Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity

Arrieta Algarra, José María and Rodríguez Bernal, Aníbal and Valero , José (2006) Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity. International Journal of Bifurcation and Chaos, 16 (10). 2965-2984 . ISSN 0218-1274

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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.

Item Type:Article
Uncontrolled Keywords:Reaction–diffusion equation; Setvalued dynamical system; Global attractor; Upper semicontinuity; Stability; Heteroclinic connections
Subjects:Sciences > Mathematics > Differential equations
ID Code:13403
Deposited On:14 Oct 2011 07:18
Last Modified:06 Feb 2014 09:48

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