Global solvability of a model for grain boundary motion with constraint

Pages: 127 - 146, Volume 5, Issue 1, February 2012

doi:10.3934/dcdss.2012.5.127       Abstract        References        Full Text (419.5K)       Related Articles

Akio Ito - Department of Electronic Engineering and Computer, Science School of Engineering, Kinki University, Takayaumenobe, Higashihiroshimashi, Hiroshima, 739-2116, Japan (email)
Nobuyuki Kenmochi - Department of Education, School of Education, Bukkyo University, 96 Kitahananobo-cho, Murasakino, Kita-ku, Kyoto, 603-8301, Japan (email)
Noriaki Yamazaki - Department of Mathematics, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, 221-8686, Japan (email)

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:  Grain boundary motion, singular diffusion, subdifferential.
Mathematics Subject Classification:  Primary: 35K45, 35K55; Secondary: 35R35.

Received: June 2009;      Revised: December 2009;      Published: February 2011.

 References