Nonlinear reaction diffusion systems of degenerate parabolic type
Copyright policy )Nonlinear reaction diffusion systems of degenerate parabolic type
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.
global existence, Epidemiology, Asymptotic behavior of solutions to PDEs, Degenerate parabolic equations, nonlinearities of gradient type, Blow-up in context of PDEs, Reaction-diffusion equations, degenerate parabolic system, Initial-boundary value problems for second-order parabolic systems, blow-up
global existence, Epidemiology, Asymptotic behavior of solutions to PDEs, Degenerate parabolic equations, nonlinearities of gradient type, Blow-up in context of PDEs, Reaction-diffusion equations, degenerate parabolic system, Initial-boundary value problems for second-order parabolic systems, blow-up
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