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arXiv · 2003.02670

Energy-dissipation in a coupled system of Allen-Cahn type equation and Kobayashi-Warren-Carter type model of grain boundary motion

Hiroshi Watanabe·Ken Shirakawa
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Abstract

In this paper, we consider a system of initial boundary value problems for parabolic equations, as a generalized version of the "$ ϕ$-$ η$-$ θ$ model" of grain boundary motion, proposed by Kobayashi [16]. The system is a coupled system of: an Allen--Cahn type equation as in (1.1) with a given temperature source; and a phase-field model of grain boundary motion, known as "Kobayashi--Warren--Carter type model". The focus of the study is on a special kind of solution, called energy-dissipative solution, which is to reproduce the energy-dissipation of the governing energy in time. Under suitable assumptions, two Main Theorems, concerned with: the existence of energy-dissipative solution; and the large-time behavior; will be demonstrated as the results of this paper.

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Hiroshi Watanabe, Ken Shirakawa. 2020-03-04. Energy-dissipation in a coupled system of Allen-Cahn type equation and Kobayashi-Warren-Carter type model of grain boundary motion. https://doi.org/10.1002/mma.6684

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