Improved Duality Estimates and Applications to Reaction-Diffusion Equations |
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| Authors: | José A Cañizo Laurent Desvillettes |
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| Institution: | 1. School of Mathematics , University of Birmingham , Edgbaston , Birmingham , UK;2. CMLA, ENS Cachan, CNRS , Cachan Cedex , France |
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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. |
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| Keywords: | Duality method Entropy method Exponential convergence to equilibrium Global existence Polynominally-in-time growing a-priori bounds Reaction-diffusion systems |
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