Global Solutions of Reaction-Diffusion Systems with a Balance Law and Nonlinearities of Exponential Growth

J. I. Kanel, M. Kirane

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23 Scopus citations

Abstract

We consider the initial boundary value problem of the form ut-aΔu=-f(u, v), vt-cΔu-dΔv=+f(u, v), x∈Ω∈RN, N≥1, t∈R+ where f(u, v)≥0, f(0, v)=0, v∈R; f(u, v)≤Kφ(u)eσv, K and σ are positive constants, φ(.) is any continuous, nonnegative, locally Lipschitzian function on R such that φ(0)=0, d>a, and c<d-a with bounded continuous nonegative initial data. This system contains in particular the Frank-Kamenetskii approximation to an nth-order exothermic chemical reaction of Arrhenius type and non-systemically autocatalysed reaction-diffusion systems. We prove the existence of global classical solutions and study their large time behaviour. Our main tools are estimates of the Neumann function for the heat equation and local Lp a priori estimates independent of time.

Original languageBritish English
Pages (from-to)24-41
Number of pages18
JournalJournal of Differential Equations
Volume165
Issue number1
DOIs
StatePublished - 20 Jul 2000

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