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arXiv · 2206.07222

Existence of solutions to a phase-field model of 3D-grain boundary motion governed by a regularized 1-harmonic type flow

Salvador Moll·Ken Shirakawa·Hiroshi Watanabe
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Abstract

In this paper we propose a quaternion formulation for the orientation variable in the three dimensional Kobayashi--Warren model for the dynamics of polycrystals. We obtain existence of solutions to the $L^2$-gradient descent flow of the constrained energy functional via several approximating problems. In particular, we use a Ginzburg-Landau type approach and some extra regularizations. Existence of solutions to the approximating problems is shown by the use of nonlinear semigroups. Coupled with good a-priori estimates, this leads to successive passages to the limit up to finally showing existence of solutions to the proposed model. Moreover, we also obtain a maximum principle for the orientation variable.

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Salvador Moll, Ken Shirakawa, Hiroshi Watanabe. 2022-06-15. Existence of solutions to a phase-field model of 3D-grain boundary motion governed by a regularized 1-harmonic type flow. https://doi.org/10.1007/s00332-023-09923-z

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