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Portugaliae Mathematica


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Volume 66, Issue 3, 2009, pp. 373–400
DOI: 10.4171/PM/1849

Published online: 2009-09-30

Nonlinear reaction diffusion systems of degenerate parabolic type

Tarik Aliziane[1], Lila Hadjadj[2] and Mohamed Said Moulay[3]

(1) USTHB, Alger, Algeria
(2) USTHB, Alger, Algeria
(3) USTHB, Alger, Algeria

In this paper we study the following parabolic problem

t(ui) − Δ(|ui|σiui) = gi(u) + \overrightarrow{bi}∇(|ui|mi − 1ui) in ]0,∞[ × Ω,
ui =0 on ]0,∞[ × ∂Ω,
ui(0,.) = ui0 in Ω,
where Ω is a bounded domain with smooth boundary and i = 1, 2,…,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.

Keywords: Global existence, blow-up, degenerate parabolic system, gradient term

Aliziane Tarik, Hadjadj Lila, Moulay Mohamed Said: Nonlinear reaction diffusion systems of degenerate parabolic type. Port. Math. 66 (2009), 373-400. doi: 10.4171/PM/1849