Ito, Akio; Kenmochi, Nobuyuki; Yamazaki, Noriaki Weak solutions of grain boundary motion model with singularity. (English) Zbl 1183.35159 Rend. Mat. Appl., VII. Ser. 29, No. 1, 51-63 (2009). 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. Cited in 5 Documents 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 Keywords:Kobayashi-Warren-Carter type; global existence PDF BibTeX XML Cite \textit{A. Ito} et al., Rend. Mat. Appl., VII. Ser. 29, No. 1, 51--63 (2009; Zbl 1183.35159) OpenURL