Lyapunov functions and Lp-estimates for a class of reaction-diffusion systems
Dirk Horstmann
Colloquium Mathematicae, Tome 89 (2001), p. 113-127 / Harvested from The Polish Digital Mathematics Library
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We give a sufficient condition for the existence of a Lyapunov function for the system aₜ = ∇(k(a,c)∇a - h(a,c)∇c), x ∈ Ω, t > 0, εcₜ=kcΔc-f(c)c+g(a,c), x ∈ Ω, t > 0, for Ω⊂ℝN, completed with either a = c = 0, or ∂a/∂n = ∂c/∂n = 0, or k(a,c) ∂a/∂n = h(a,c) ∂c/∂n, c = 0 on ∂Ω × t > 0. Furthermore we study the asymptotic behaviour of the solution and give some uniform Lp-estimates.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:283757 
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     year = {2001},
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Dirk Horstmann. Lyapunov functions and $L^{p}$-estimates for a class of reaction-diffusion systems. Colloquium Mathematicae, Tome 89 (2001) pp. 113-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-1-7/