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

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2009, 2009(Special): 486-495. doi: 10.3934/proc.2009.2009.486

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

Hirotoshi Kuroda ^1, and Noriaki Yamazaki ^2,

1.	Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8,, Kita-ku, Sapporo, Hokkaido, 060-0810, Japan
2.	Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama, 221-8686, Japan

Received July 2008 Revised April 2009 Published September 2009

Abstract
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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, numerical experiments, vectorial singular diffusion.

Mathematics Subject Classification: Primary: 35K55, 65M99; Secondary: 35R35.

Citation: Hirotoshi Kuroda, Noriaki Yamazaki. Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations. Conference Publications, 2009, 2009 (Special) : 486-495. doi: 10.3934/proc.2009.2009.486

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