Geodesic
A phase-field model of grain boundary motion
Applications of Mathematics, Tome 53 (2008) no. 5, pp. 433-454.

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We consider a phase-field model of grain structure evolution, which appears in materials 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.
DOI : 10.1007/s10492-008-0035-8
Classification : 35D05, 35K45, 35K50, 35K55, 35R35
Keywords: grain boundary motion; singular diffusion; subdifferential 
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Ito, Akio; Kenmochi, Nobuyuki; Yamazaki, Noriaki. A phase-field model of grain boundary motion. Applications of Mathematics, Tome 53 (2008) no. 5, pp. 433-454. doi : 10.1007/s10492-008-0035-8. http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0035-8/

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