IJPAM: Volume 86, No. 5 (2013)

EXISTENCE AND UNIQUENESS 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 this paper, we shall prove the existence and uniqueness of radial solutions for the nonhomogeneous elliptic equation

\begin{displaymath} div\left( \left\vert \nabla u\right\vert ^{p-2}\nabla u\righ... ...ert ^l\left\vert u\right\vert ^{q-1}u=0,\quad x\in \Bbb{R}^N, \end{displaymath}

These solutions are related to self-similar solutions of the degenerate parabolic equation

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

where p >2, q ≥ 1, N ≥ 1, -p < l, -N < l.

Received: May 15, 2013

AMS Subject Classification: 35K55, 35K65

Key Words and Phrases: elliptic problem, parabolic problem, nonhomogeneous equation, self-similar solution, existence, uniqueness

Download paper from here.


DOI: 10.12732/ijpam.v86i5.8 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