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

• Autorzy: Noureddine Igbida , Mokhtar Kirane
• Języki publikacji: EN

Abstrakty

EN

This paper provides blow up results of Fujita type for a reaction-diffusion system of 3 equations in the form $uₜ - Δ(a_{11}u) = h(t,x)|v|^{p}$, $vₜ -Δ(a_{21}u) - Δ(a_{22}v) = k(t,x)|w|^{q}$, $wₜ - Δ(a_{31}u) - Δ(a_{32}v) - Δ(a_{33}w) = l(t,x)|u|^{r}$, for $x ∈ ℝ^{N}$, t > 0, p > 0, q > 0, r > 0, $a_{ij} = a_{ij}(t,x,u,v)$, under initial conditions u(0,x) = u₀(x), v(0,x) = v₀(x), w(0,x) = w₀(x) for $x ∈ ℝ^{N}$, 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.

Kategorie tematyczne

• 35K57: Reaction-diffusion equations
• 35B33: Critical exponents

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 92
• Numer: 1
• Strony: 87-96

Daty

wydano

2002

Twórcy

autor

Noureddine Igbida

• Faculté de Mathématiques et d'Informatique, LAMFA, CNRS FRE 2270, Université de Picardie-Jules Verne, 33 rue Saint Leu, 80038 Amiens, France

autor

Mokhtar Kirane

• Faculté de Mathématiques et d'Informatique, LAMFA, CNRS FRE 2270, Université de Picardie-Jules Verne, 33 rue Saint Leu, 80038 Amiens, France
• Laboratoire de Mathématiques, Pôle Sciences et Technologies, Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex, France

Identyfikatory

DOI

10.4064/cm92-1-8