Article Contents

2012, Volume 5, Issue 1: 127-146. Doi: 10.3934/dcdss.2012.5.127

This issue Previous Article Reaction diffusion equation with non-local term arises as a mean field limit of the master equation Next Article A relation between cross-diffusion and reaction-diffusion

Global solvability of a model for grain boundary motion with constraint

1.
Department of Electronic Engineering and Computer, Science School of Engineering, Kinki University, Takayaumenobe, Higashihiroshimashi, Hiroshima, 739-2116
2.
Department of Education, School of Education, Bukkyo University, 96 Kitahananobo-cho, Murasakino, Kita-ku, Kyoto, 603-8301
3.
Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, 221-8686

Received: June 2009

Revised: December 2009

Published: February 2012

Abstract / Introduction Related Papers Cited by

Abstract

We consider a model for grain boundary motion with constraint. In composite material science it is very important to investigate the grain boundary formation and its dynamics. In this paper we study a phase-filed model of grain boundaries, which is a modified version of the one proposed by R. Kobayashi, J.A. Warren and W.C. Carter [18]. The model is described as a system of a nonlinear parabolic partial differential equation and a nonlinear parabolic variational inequality. The main objective of this paper is to show the global existence of a solution for our model, employing some subdifferential techniques in the convex analysis.

Keywords:

Mathematics Subject Classification: Primary: 35K45, 35K55; Secondary: 35R35.

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