Improved duality estimates and applications to reaction-diffusion equations

José A. Cañizo; Laurent Desvillettes; Klemens Fellner

doi:10.1080/03605302.2013.829500

Improved duality estimates and applications to reaction-diffusion equations

José A. Cañizo, Laurent Desvillettes, Klemens Fellner

Mathematics

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52 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	1185-1204
Journal	Communications in Partial Differential Equations
Volume	39
Issue number	6
Early online date	2 Sept 2013
DOIs	https://doi.org/10.1080/03605302.2013.829500
Publication status	Published - 1 May 2014

Keywords

math.AP
35B45, 35Q72, 82D60

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10.1080/03605302.2013.829500

Canizo_2013_ImprovedDualityEstimates_ArxivSubmitted manuscript, 271 KBLicence: None: All rights reserved

http://arxiv.org/abs/1304.4040v1

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AU - Desvillettes, Laurent

AU - Fellner, Klemens

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Y1 - 2014/5/1

N2 - 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.

AB - 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.

KW - math.AP

KW - 35B45, 35Q72, 82D60

U2 - 10.1080/03605302.2013.829500

DO - 10.1080/03605302.2013.829500

M3 - Article

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SP - 1185

EP - 1204

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 6

ER -

Improved duality estimates and applications to reaction-diffusion equations

Abstract

Keywords

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