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Weak solutions of grain boundary motion model with singularity. (English) Zbl 1183.35159

Summary: We consider the grain boundary motion model of Kobayashi-Warren-Carter type, which arises in material sciences. The system, which consists of two nonlinear parabolic PDEs with singularity, is of the phase-field type. In this paper we show the global existence of solutions for our model in a weak variational sense.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35R35 Free boundary problems for PDEs
35D30 Weak solutions to PDEs
35K59 Quasilinear parabolic equations
35K67 Singular parabolic equations
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