In this paper we study the following parabolic problem

$$
\begin{cases}
∂t(u_i) − Δ(|u_i|^{σ_i}u_i) = g_i(u) + \overrightarrow{b_i}∇(|ui|^{m_i − 1}u_i) | &\text{in } ]0,∞[×Ω,\\
u_i =0 &\text{on }]0,∞[×∂Ω,\\
u_i(0,.) = u_{i0} &\text{in }Ω,
\end{cases}
$$

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.

Nonlinear reaction diffusion systems of degenerate parabolic type

Tarik Aliziane

Lila Hadjadj

Mohamed Said Moulay

Abstract

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