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A phase-field model of grain boundary motion. (English) Zbl 1199.35138
Summary: We consider a phase-field model of grain structure evolution, which appears in material 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.

MSC:
35K45 Initial value problems for second-order parabolic systems
35K55 Nonlinear parabolic equations
35R35 Free boundary problems for PDEs
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