## 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

### Keywords:

grain boundary motion; singular diffusion; subdifferential
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### References:

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