Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 80, pp. 1-22.
Title: Self similar solutions of generalized Burgers equation
Authors: Abdelilah Gmira (Univ. Abdelmalek Essaadi, Maroc)
Ahmed Hamydy (Univ. Abdelmalek Essaadi, Maroc)
Salek Ouailal (Univ. Abdelmalek Essaadi, Maroc)
Abstract:
In this paper, we study the initial-value problem
\begin{gather*}
(|u'|^{p-2}u')'+\beta r u'+\alpha u-\gamma |u|^{q-1}u|u'|^{p-2}u'=0,
\quad r>0, \\
u(0)=A,\quad u'(0)=0,
\end{gather*}
where $A>0$, $p>2$, $q>1$, $\alpha>0$, $\beta>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