Analysis and explicit solvability of degenerate tensorial problems
Abstract We study a two-dimensional boundary value problem described by a tensorial equation in a bounded domain. Once its more general definition is given, we conclude that its analysis is linked to the resolution of an overdetermined hyperbolic problem and hence present some discussions and consid...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-017-0920-8 |
| _version_ | 1819267058779553792 |
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| author | Tongxing Li Giuseppe Viglialoro |
| author_facet | Tongxing Li Giuseppe Viglialoro |
| author_sort | Tongxing Li |
| collection | DOAJ |
| description | Abstract We study a two-dimensional boundary value problem described by a tensorial equation in a bounded domain. Once its more general definition is given, we conclude that its analysis is linked to the resolution of an overdetermined hyperbolic problem and hence present some discussions and considerations. Secondly, for a simplified version of the original formulation, which leads to a degenerate problem on a rectangle, we prove the existence and uniqueness of a solution under proper assumptions on the data. |
| first_indexed | 2024-12-23T21:11:08Z |
| format | Article |
| id | doaj.art-abaf046a445f491cbfe3b7c620c9ca8a |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-23T21:11:08Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-abaf046a445f491cbfe3b7c620c9ca8a2022-12-21T17:31:03ZengSpringerOpenBoundary Value Problems1687-27702018-01-012018111310.1186/s13661-017-0920-8Analysis and explicit solvability of degenerate tensorial problemsTongxing Li0Giuseppe Viglialoro1School of Information Science and Engineering, Linyi UniversityDipartimento di Matematica e Informatica, Università di CagliariAbstract We study a two-dimensional boundary value problem described by a tensorial equation in a bounded domain. Once its more general definition is given, we conclude that its analysis is linked to the resolution of an overdetermined hyperbolic problem and hence present some discussions and considerations. Secondly, for a simplified version of the original formulation, which leads to a degenerate problem on a rectangle, we prove the existence and uniqueness of a solution under proper assumptions on the data.http://link.springer.com/article/10.1186/s13661-017-0920-8degenerate hyperbolic equationsboundary value problems |
| spellingShingle | Tongxing Li Giuseppe Viglialoro Analysis and explicit solvability of degenerate tensorial problems Boundary Value Problems degenerate hyperbolic equations boundary value problems |
| title | Analysis and explicit solvability of degenerate tensorial problems |
| title_full | Analysis and explicit solvability of degenerate tensorial problems |
| title_fullStr | Analysis and explicit solvability of degenerate tensorial problems |
| title_full_unstemmed | Analysis and explicit solvability of degenerate tensorial problems |
| title_short | Analysis and explicit solvability of degenerate tensorial problems |
| title_sort | analysis and explicit solvability of degenerate tensorial problems |
| topic | degenerate hyperbolic equations boundary value problems |
| url | http://link.springer.com/article/10.1186/s13661-017-0920-8 |
| work_keys_str_mv | AT tongxingli analysisandexplicitsolvabilityofdegeneratetensorialproblems AT giuseppeviglialoro analysisandexplicitsolvabilityofdegeneratetensorialproblems |