Solvability for the non-isothermal Kobayashi–Warren–Carter system

Solvability for the non-isothermal Kobayashi–Warren–Carter system

In this paper, a system of parabolic type initial-boundary value problems are considered. The system (S)$_\nu$ is based on the non-isothermal model of grain boundary motion by <sup>[<span class="xref"><a href="javascript:;" ref-type="bibr" orgid="R38...

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Bibliographic Details
Main Authors: Ken Shirakawa, HiroshiWatanabe
Format: Article
Language:English
Published: AIMS Press 2017-03-01
Series:AIMS Mathematics
Subjects:
Non-isothermal grain boundary motion| Kobayashi–Warren–Carter type model| existence of L2-based solution| weighted total variation| time-discretization
Online Access:http://www.aimspress.com/article/10.3934/Math.2017.1.161/fulltext.html
Description
Summary:In this paper, a system of parabolic type initial-boundary value problems are considered. The system (S)$_\nu$ is based on the non-isothermal model of grain boundary motion by <sup>[<span class="xref"><a href="javascript:;" ref-type="bibr" orgid="R38">38</a></span>]</sup>, which was derived as an extending version of the ``Kobayashi--Warren--Carter model'' of grain boundary motion by <sup>[<span class="xref"><a href="javascript:;" ref-type="bibr" orgid="R23">23</a></span>]</sup>. Under suitable assumptions, the existence theorem of $ L^2 $-based solutions is concluded, as a versatile mathematical theory to analyze various Kobayashi--Warren--Carter type models.
ISSN:2473-6988

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