Improved duality estimates and applications to reaction-diffusion equations

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Colleges, School and Institutes


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 languageEnglish
Pages (from-to)1185-1204
JournalCommunications in Partial Differential Equations
Issue number6
Early online date2 Sep 2013
Publication statusPublished - 1 May 2014


  • math.AP, 35B45, 35Q72, 82D60