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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| Format: | Article |
| Language: | English |
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AIMS Press
2017-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/10.3934/Math.2017.1.161/fulltext.html |
| _version_ | 1828852786361532416 |
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| author | Ken Shirakawa HiroshiWatanabe |
| author_facet | Ken Shirakawa HiroshiWatanabe |
| author_sort | Ken Shirakawa |
| collection | DOAJ |
| description | 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 $-based solutions is concluded, as a versatile mathematical theory to analyze various Kobayashi--Warren--Carter type models. |
| first_indexed | 2024-12-13T00:00:34Z |
| format | Article |
| id | doaj.art-c8732dff68a144778c6bcf760b59ec64 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T00:00:34Z |
| publishDate | 2017-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c8732dff68a144778c6bcf760b59ec642022-12-22T00:06:25ZengAIMS PressAIMS Mathematics2473-69882017-03-012116119410.3934/Math.2017.1.161Solvability for the non-isothermal Kobayashi–Warren–Carter systemKen Shirakawa0HiroshiWatanabe11 Department of Mathematics, Faculty of Education, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan2 Department of Computer Science and Intelligent Systems, Faculty of Engineering, Oita University, 700 Dannoharu, Oita, 870-1192, JapanIn this paper, a system of parabolic type initial-boundary value problems are considered. The system (S)$_\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.http://www.aimspress.com/article/10.3934/Math.2017.1.161/fulltext.htmlNon-isothermal grain boundary motion| Kobayashi–Warren–Carter type model| existence of L2-based solution| weighted total variation| time-discretization |
| spellingShingle | Ken Shirakawa HiroshiWatanabe Solvability for the non-isothermal Kobayashi–Warren–Carter system AIMS Mathematics Non-isothermal grain boundary motion| Kobayashi–Warren–Carter type model| existence of L2-based solution| weighted total variation| time-discretization |
| title | Solvability for the non-isothermal Kobayashi–Warren–Carter system |
| title_full | Solvability for the non-isothermal Kobayashi–Warren–Carter system |
| title_fullStr | Solvability for the non-isothermal Kobayashi–Warren–Carter system |
| title_full_unstemmed | Solvability for the non-isothermal Kobayashi–Warren–Carter system |
| title_short | Solvability for the non-isothermal Kobayashi–Warren–Carter system |
| title_sort | solvability for the non isothermal kobayashi warren carter system |
| topic | Non-isothermal grain boundary motion| Kobayashi–Warren–Carter type model| existence of L2-based solution| weighted total variation| time-discretization |
| url | http://www.aimspress.com/article/10.3934/Math.2017.1.161/fulltext.html |
| work_keys_str_mv | AT kenshirakawa solvabilityforthenonisothermalkobayashiwarrencartersystem AT hiroshiwatanabe solvabilityforthenonisothermalkobayashiwarrencartersystem |