IJPAM: Volume 86, No. 5 (2013)

QUALITATIVE PROPERTIES OF SELF-SIMILAR
SOLUTIONS OF A NONHOMOGENEOUS EQUATION

Badia Hamri1, Abdelilah Gmira2, Youssef Jabri3
1,2Department of Mathematics
Faculty of Science
University Abdelmalek Essaâdi
B.P. 2121, Tétouan, MOROCCO
3Department of Mathematics
National School of Applied Sciences
University Mohammed I
B.P. 669, Oujda, MOROCCO


Abstract. In [#!A2!#], we have proved the existence and uniqueness of self-similar radially symmetric solutions for the nonhomogeneous equation

\begin{displaymath} u_t=div\left( \left\vert \nabla u\right\vert ^{p-2}\nabla u\... ...ght\vert ^{q-1}u,\quad (t,x)\in (0,+\infty )\times \Bbb{R}^N. \end{displaymath}

where p>2, q ≥ 1, N ≥ 1, -p<l, -N<l.

We have studied the asymptotic behaviour of such a solution in [3]. Our aim, in this paper, is to classify the solutions (positiveness, compact support,...) according to the parameters p, q and l.

Received: May 15, 2013

AMS Subject Classification: 35K55, 35K65

Key Words and Phrases: qualitative properties, self-similar solution, parabolic problem, nonhomogeneous equation

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DOI: 10.12732/ijpam.v86i5.9 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 5