Global solvability of a model for grain boundary motion with
Akio Ito - Department of Electronic Engineering and Computer, Science School of Engineering, Kinki University, Takayaumenobe, Higashihiroshimashi, Hiroshima, 739-2116, 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 . 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.
Received: June 2009; Revised: December 2009; Published: February 2011.