Blow up for a completely coupled Fujita type reaction-diffusion system

Noureddine Igbida, Mokhtar Kirane

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This paper provides blow up results of Fujita type for a reaction-diffusion system of 3 equations in the form ut − Δ(a11u) = h(t, x)|v|p, vt − Δ (a21u) − Δ(a22v) = k(t, x)|w|q, wt − Δ(a31u) − Δ(a32v) − Δ(a33w) = l(t, x)|u|r, for x ∈ ℝN, t > 0, p > 0, q > 0, r > 0, aij = aij (t, x, u, v), under initial conditions u(0, x) = u0(x), v(0, x) = v0(x),w(0, x) = w0(x) for x ∈ ℝN, where u0, v0,w0 are nonnegative, continuous and bounded functions. Subject to conditions on dependence on the parameters p, q, r,N and the growth of the functions h, k, l at infinity, we prove finite blow up time for every solution of the above system, generalizing results of H. Fujita for the scalar Cauchy problem, of M. Escobedo and M. A. Herrero, of Fila, Levine and Uda, and of J. Rencławowicz for systems.

Original languageBritish English
Pages (from-to)87-96
Number of pages10
JournalColloquium Mathematicum
Volume92
Issue number1
DOIs
StatePublished - 2002

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