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Improved duality estimates and applications to reaction-diffusion equations

Pré-print du CMLA 2013-07 - version du 15 avril 2013

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Auteurs : José A. Canizo, Laurent Desvillettes, Klemens Fellner

Abstract :

We present a refined duality estimate for parabolic equations. This estimate entails new results for systems of reaction-diffusion equations, including smoothness and exponential convergence towards equilibrium for equations with quadratic right-hand sides in two dimensions.

For general systems in any space dimension, we obtain smooth solutions of reaction-diffusion systems coming out of reversible chemistry under an assumption that the diffusion coefficients are sufficiently close one to another.
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