Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations

Pages: 486 - 495, Issue Special, September 2009

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Hirotoshi Kuroda - Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8,, Kita-ku, Sapporo, Hokkaido, 060-0810, Japan (email)
Noriaki Yamazaki - Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama, 221-8686, Japan (email)

Abstract: We consider a vectorial nonlinear diffusion equation with inhomogeneous terms in one-dimensional space. In this paper we study approximating problems of singular diffusion equations with a piecewise constant initial data. Also we consider the relationship between the singular diffusion problem and its approximating ones. Moreover we give some numerical experiments for the approximating equation with inhomogeneous terms and a piecewise constant initial data.

Keywords:  Approximating problems, vectorial singular diffusion, numerical experiments
Mathematics Subject Classification:  Primary: 35K55, 65M99; Secondary: 35R35

Received: July 2008;      Revised: April 2009;      Published: September 2009.