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Zbl 1163.35424
Hamydy, Ahmed
The existence and the asymptotic behavior of traveling waves solutions for a strongly nonlinear equation. (L'existence et le comportement asymptotique des solutions d'ondes progressives pour une équation fortement non linéaire.) (French)
[J] Ann. Math. Blaise Pascal 15, No. 1, 29-41 (2008). ISSN 1259-1734

Summary: We study the existence and the asymptotic behavior of traveling waves solutions for the equation $U_{t} = A(|U_{x}|^{p-2}U_{x})_{x} + KU^{q}$. We prove that these solutions exist if and only if $q < 1$ and $c < 0$ or $q \leq p-1$ and $c > 0$. We introduce also the asymptotic behavior of these solutions.

MSC 2000:: *35K65 Parabolic equations of degenerate type
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions of PDE

Keywords: diffusion; absorption; strongly nonlinear equation; travelling wave; asymptotic behavior

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