JournalspmVol. 66 , No. 3DOI 10.4171/pm/1849

Nonlinear reaction diffusion systems of degenerate parabolic type

  • Tarik Aliziane

    USTHB, Alger, Algeria
  • Lila Hadjadj

    USTHB, Alger, Algeria
  • Mohamed Said Moulay

    USTHB, Alger, Algeria
Nonlinear reaction diffusion systems of degenerate parabolic type cover

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Abstract

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 =0on ]0,∞[ × ∂Ω,
ui(0,.) = ui0in 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.