期刊
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
卷 39, 期 6, 页码 1185-1204出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2013.829500
关键词
Duality method; Entropy method; Exponential convergence to equilibrium; Global existence; Polynominally-in-time growing a-priori bounds; Reaction-diffusion systems; 35B45; 35B40; 35D57
资金
- MINECO [MTM2011-27739-C04-02]
- Marie-Curie CIG project KineticCF
- NAWI Graz
- Austrian Science Fund (FWF) [W1244] Funding Source: Austrian Science Fund (FWF)
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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