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Solvability for the non-isothermal Kobayashi-Warren-Carter system. (English) Zbl 1427.35150

Summary: In this paper, a system of parabolic type initial-boundary value problems are considered. The system \((\mathrm{S})_\nu\) is based on the non-isothermal model of grain boundary motion by J. A. Warren et al., [“Extending phase field models of solidification to polycrystalline materials”, Acta Materialia 51, No. 20, 6035–6058 (2003; doi:10.1016/S1359-6454(03)00388-4)], which was derived as an extending version of the “Kobayashi-Warren-Carter model” of grain boundary motion by R. Kobayashi et al. [in: Proceedings of the international conference on free boundary problems: theory and applications, Chiba, Japan, November 7–13, 1999. II. Tokyo: Gakkotosho. 283–294 (2000; Zbl 0961.35164)]. Under suitable assumptions, the existence theorem of \(L^2\)-based solutions is concluded, as a versatile mathematical theory to analyze various Kobayashi-Warren-Carter type models.

MSC:

35K87 Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators
35R06 PDEs with measure
35K67 Singular parabolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence

Citations:

Zbl 0961.35164
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References:

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