Nonlinear reaction diffusion systems of degenerate parabolic type

Tarik Aliziane; Lila Hadjadj; Mohamed Said Moulay

doi:10.4171/pm/1849

JournalspmVol. 66, No. 3pp. 373–400

Nonlinear reaction diffusion systems of degenerate parabolic type

Tarik Aliziane
USTHB, Alger, Algeria
Lila Hadjadj
USTHB, Alger, Algeria
Mohamed Said Moulay
USTHB, Alger, Algeria

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Abstract

In this paper we study the following parabolic problem

⎩ ⎨ ⎧ \partial t (u_{i}) - Δ (∣ u_{i} ∣^{σ_{i}} u_{i}) = g_{i} (u) + b_{i} \nabla (∣ u i ∣^{m_{i} - 1} u_{i}) ∣ u_{i} = 0 u_{i} (0, .) = u_{i 0} in] 0, \infty [\times Ω, on] 0, \infty [\times \partial Ω, in Ω,

where $Ω$ is a bounded domain with smooth boundary and $i = 1, 2, \dots, d$ . Our aim is to study existence of globally bounded weak solutions or blow-up, depending on the relations between the parameters that appear in the problem.

Cite this article

Tarik Aliziane, Lila Hadjadj, Mohamed Said Moulay, Nonlinear reaction diffusion systems of degenerate parabolic type. Port. Math. 66 (2009), no. 3, pp. 373–400

DOI 10.4171/PM/1849