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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
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- In this paper, we consider a system of initial boundary value problems for parabolic equations, as a generalized version of the "$ \phi $-$ \eta $-$ \theta $ 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.<br />Comment: 37 pages. arXiv admin note: text overlap with arXiv:1408.4204
- Subjects :
- General Mathematics
010102 general mathematics
Mathematical analysis
General Engineering
Motion (geometry)
Dissipation
Type (model theory)
01 natural sciences
Parabolic partial differential equation
010101 applied mathematics
Mathematics - Analysis of PDEs
35K87, 35R06, 35K67
FOS: Mathematics
Grain boundary
Boundary value problem
0101 mathematics
Focus (optics)
Energy (signal processing)
Mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....be163826d9713114540274e4f5f6d275
- Full Text :
- https://doi.org/10.48550/arxiv.2003.02670