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