Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024584 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 23 Pages |
Abstract
We study general quadratic reaction-diffusion systems with detailed balance, in space dimension dâ¤4. We show that close-to-equilibrium solutions (in an L2 sense) are regular for all times, and that they relax to equilibrium exponentially in a strong sense. That is: all detailed balance equilibria are exponentially asymptotically stable in all Lp norms, at least in dimension dâ¤4. The results are given in detail for the four-species reaction-diffusion system, where the involved constants can be estimated explicitly. The main novelty is the regularity result and exponential relaxation in Lp norms for p>1, which up to our knowledge is new in dimensions 3 and 4.
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Authors
MarÃa J. Cáceres, José A. Cañizo,