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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
Hiroshi Watanabe
Oita University
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Ken Shirakawa
Chiba University
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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.

Peer review status:ACCEPTED

02 Mar 2020Submitted to Mathematical Methods in the Applied Sciences
07 Mar 2020Submission Checks Completed
07 Mar 2020Assigned to Editor
07 Mar 2020Reviewer(s) Assigned
14 Jun 2020Review(s) Completed, Editorial Evaluation Pending
15 Jun 2020Editorial Decision: Revise Minor
23 Jun 20201st Revision Received
23 Jun 2020Submission Checks Completed
23 Jun 2020Assigned to Editor
23 Jun 2020Editorial Decision: Accept