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 |
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Pages (from-to) | 1185-1204 |
Journal | Communications in Partial Differential Equations |
Volume | 39 |
Issue number | 6 |
Early online date | 2 Sept 2013 |
DOIs | |
Publication status | Published - 1 May 2014 |
Keywords
- math.AP
- 35B45, 35Q72, 82D60