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

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Igbida N., Kirane M.

Colloquium Mathematicum

2002

tom 92

nr 1

87-96

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Igbida N.

1 Kirane M.

1 2002

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