# American Institute of Mathematical Sciences

February  2012, 5(1): 127-146. doi: 10.3934/dcdss.2012.5.127

## 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, Japan 3 Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, 221-8686, Japan

Received  June 2009 Revised  December 2009 Published  February 2011

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.
Citation: Akio Ito, Nobuyuki Kenmochi, Noriaki Yamazaki. Global solvability of a model for grain boundary motion with constraint. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 127-146. doi: 10.3934/dcdss.2012.5.127
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##### References:
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