A. Ito, Department of Electronic Engineering and Computer Science, School of Engineering, Kinki University, 1, Takayaumenobe, Higashihiroshima, Hiroshima, 739-2116, Japan, e-mail: aito@hiro.kindai.ac.jp; N. Kenmochi, Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan, e-mail: kenmochi@faculty.chiba-u.jp; N. Yamazaki, Department of Mathematical Science, Common Subject Division, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, 050-8585, Japan, e-mail: noriaki@mmm.muroran-it.ac.jp
Abstract: We consider a phase-field model of grain structure evolution, which appears in materials sciences. In this paper we study the grain boundary motion model of Kobayashi-Warren-Carter type, which contains a singular diffusivity. The main objective of this paper is to show the existence of solutions in a generalized sense. Moreover, we show the uniqueness of solutions for the model in one-dimensional space.
Keywords: grain boundary motion, singular diffusion, subdifferential
Classification (MSC 2000): 35K45, 35K55, 35R35
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