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

Noureddine Igbida, and Mokhtar Kirane. "Blow up for a completely coupled Fujita type reaction-diffusion system." Colloquium Mathematicae 92.1 (2002): 87-96. <http://eudml.org/doc/284242>.

@article{NoureddineIgbida2002,
abstract = {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.},
author = {Noureddine Igbida, Mokhtar Kirane},
journal = {Colloquium Mathematicae},
keywords = {system of three equations},
language = {eng},
number = {1},
pages = {87-96},
title = {Blow up for a completely coupled Fujita type reaction-diffusion system},
url = {http://eudml.org/doc/284242},
volume = {92},
year = {2002},
}

TY - JOUR
AU - Noureddine Igbida
AU - Mokhtar Kirane
TI - Blow up for a completely coupled Fujita type reaction-diffusion system
JO - Colloquium Mathematicae
PY - 2002
VL - 92
IS - 1
SP - 87
EP - 96
AB - 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.
LA - eng
KW - system of three equations
UR - http://eudml.org/doc/284242
ER -