April  1999, 5(2): 399-424. doi: 10.3934/dcds.1999.5.399

Finite dimensional attractors for reaction-diffusion equations in $R^n$ with a strong nonlinearity

1. 

Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, 14195 Berlin, Germany

2. 

Université de Poitiers, L3MA, SP2MI, Boulevard 3 - Téléport 2, B. P. 179, 86960 Futuroscope Cedex, France

Received  March 1998 Revised  June 1998 Published  January 1999

Our aim in this article is to study the long time behavior of a class of reaction-diffusion equations in the whole space for which the nonlinearity depends explicitly on the gradient of the unknown function. We prove the existence of the global attractor and of exponential attractors for the semigroup associated with the equation. We also consider the nonautonomous case, and when the forcing term depends quasiperiodically on the time, we prove the existence of uniform and uniform exponential attractors.
Citation: Messoud Efendiev, Alain Miranville. Finite dimensional attractors for reaction-diffusion equations in $R^n$ with a strong nonlinearity. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 399-424. doi: 10.3934/dcds.1999.5.399
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