Large-time behavior for a PDE model of isothermal grain boundary motion with a constraint

Ken Shirakawa; Hiroshi Watanabe

doi:10.3934/proc.2015.1009

Article Contents

2015, Volume 2015: 1009-1018. Doi: 10.3934/proc.2015.1009 open access

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Large-time behavior for a PDE model of isothermal grain boundary motion with a constraint

Ken Shirakawa^1, and
Hiroshi Watanabe^2,

1.
Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522
2.
Department of General Education, Salesian Polytechnic, 4-6-8 Oyamagaoka, Machida-city, Tokyo, 194-0215

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

In this paper, a system of parabolic initial-boundary value problems is considered as a possible PDE model of isothermal grain boundary motion. The solvability of this system was proved in [preprint, arXiv:1408.4204., by means of the notion of weighted total variation. In this light, we set our goal to prove two main theorems, which are concerned with the $ \Gamma $-convergence for time-dependent versions of the weighted total variations, and the large-time behavior of solution.

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Mathematics Subject Classification: Primary: 35B40, 35K87; Secondary: 35K67.

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References

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