Electron. J. Diff. Eqns., Vol. 2005(2005), No. 80, pp. 1-22.

Self similar solutions of generalized Burgers equation

Abdelilah Gmira, Ahmed Hamydy, Salek Ouailal

Abstract:
In this paper, we study the initial-value problem
$$\displaylines{ (|u'|^{p-2}u')'+\beta r u'+\alpha u-\gamma |u|^{q-1}u|u'|^{p-2}u'=0, \quad r greater than 0, \cr u(0)=A,\quad u'(0)=0, }$$
where $A$ greater than 0, $p$ greater than 2, $q greater than 1, $\alpha greater than 0, $\beta greater than 0 and $ \gamma \in{\mathbb{R}}$. Existence and complete classification of solutions are established. Asymptotic behavior for nonnegative solutions is also presented.

Submitted December 6, 2004. Published July 15, 2005.
Math Subject Classifications: 35k55, 35k65.
Key Words: Burgers equation; self similar; classification; asymptotic behavior

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Abdelilah Gmira
Universite Abdelmalek Essaadi, Faculte des Sciences
Departement de Mathematiques et informatique
B. P. 2121 Tetouan - Maroc
email: gmira@fst.ac.ma
Ahmed Hamydy
Universite Abdelmalek Essaadi, Faculte des Sciences
Departement de Mathematiques et informatique
B. P. 2121 Tetouan - Maroc
email: hamydy@caramail.com
Salek Ouailal
Universite Abdelmalek Essaadi, Faculte des Sciences
Departement de Mathematiques et informatique
B. P. 2121 Tetouan - Maroc
email: salekouailal@yahoo.com

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