L’existence et le comportement asymptotique des solutions d’ondes progressives pour une équation fortement non linéaire

Hamydy, Ahmed

Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 1, pp. 29-41.

Dans ce papier on étudie l’existence et le comportement asymptotique des solutions de type ondes progressives à propagations finies de l’équation $U_t=A{\left({\left|U_x\right|}^{p-2}{U}_x\right)}_x+K{U}^q$. On prouve que ces solutions existent si et seulement si $q<1$ et $c<0$ ou bien $q\le p-1$ et $c>0$. On donne aussi le comportement asymptotique de ces solutions.

In this paper we study the existence and the asymptotic behavior of traveling waves solutions for the equation $U_t=A{\left({\left|U_x\right|}^{p-2}{U}_x\right)}_x+K{U}^q$. We prove that these solutions exist if and only if $q<1$ and $c<0$ or $q\le p-1$ and $c>0$. We introduce also the asymptotic behavior of these solutions.

Classification : 35K55, 35K65
Mot clés : Diffusion, Absorption, fortement non linéaire, Solution d’onde, Comportement asymptotique
Keywords: Diffusion, Absorption, strongly nonlinear equation, Travelling wave, asymptotic behavior

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