IJPAM: Volume 61, No. 3 (2010)

THE INITIAL VALUE SEMILINEAR
DIFFUSION EQUATIONS ON ORLICZ SPACES

Tor A. Kwembe$^1$, Paul Musial$^2$
Department of Mathematics
Jackson State University
P.O. Box 17610, Jackson, MS 39217-0410, USA
e-mail: [email protected]
Department of Mathematics and Computer Science
Chicago State University
9501, South King Drive, Chicago, IL 60628, USA
e-mail: [email protected]


Abstract.This paper is an extension of the L$^{\text{p}}$ solutions of an initial value semilinear diffusion equation to include Orlicz spaces. It is shown that if $\Phi$ is a $\bigtriangleup_{\text{2}}$N-function such that the initial value belongs to L$^{\Phi}$(R$^{\text{n}}$), then the maximal solution u$^{\text{*}}$ of the initial value problem belongs to L$^{\Phi}%
$(R$^{\text{n}}$) and is unique. Some regularity and almost everywhere point-wise convergence results in L$^{\Phi}$(R$^{\text{n}}$) are also given.

Received: March 5, 2010

AMS Subject Classification: 31B10, 35G10, 35C15, 35D10, 46E35

Key Words and Phrases: Orlicz spaces, semiliear diffusion equation, regularity, maximal solution

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 3