Global Solutions for a Simplified Shallow Elastic Fluids Model
The Cauchy problem for a simplified shallow elastic fluids model, one 3×3 system of Temple’s type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Rie...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/920248 |
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| _version_ | 1850213107722354688 |
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| author | Yun-guang Lu Christian Klingenberg Leonardo Rendon De-Yin Zheng |
| author_facet | Yun-guang Lu Christian Klingenberg Leonardo Rendon De-Yin Zheng |
| author_sort | Yun-guang Lu |
| collection | DOAJ |
| description | The Cauchy problem for a simplified shallow elastic fluids model, one 3×3 system of Temple’s type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Riemann invariant is singular near the zero layer depth ρ=0. This work extends in some sense the previous works, (Serre, 1987) and (Leveque and Temple, 1985), which provided the global existence of weak solutions for 2×2 strictly hyperbolic system and (Heibig, 1994) for n×n strictly hyperbolic system with smooth Riemann invariants. |
| format | Article |
| id | doaj-art-8ba202030b2b439ca7c764db8e28a5c9 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8ba202030b2b439ca7c764db8e28a5c92025-08-20T02:09:11ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/920248920248Global Solutions for a Simplified Shallow Elastic Fluids ModelYun-guang Lu0Christian Klingenberg1Leonardo Rendon2De-Yin Zheng3Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, ChinaInstitute of Mathematics, University of Wurzburg, Emil Fischer Straße 30, 97074 Wurzburg, GermanyDepartamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, ColombiaDepartment of Mathematics, Hangzhou Normal University, Hangzhou 310036, ChinaThe Cauchy problem for a simplified shallow elastic fluids model, one 3×3 system of Temple’s type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Riemann invariant is singular near the zero layer depth ρ=0. This work extends in some sense the previous works, (Serre, 1987) and (Leveque and Temple, 1985), which provided the global existence of weak solutions for 2×2 strictly hyperbolic system and (Heibig, 1994) for n×n strictly hyperbolic system with smooth Riemann invariants.http://dx.doi.org/10.1155/2014/920248 |
| spellingShingle | Yun-guang Lu Christian Klingenberg Leonardo Rendon De-Yin Zheng Global Solutions for a Simplified Shallow Elastic Fluids Model Abstract and Applied Analysis |
| title | Global Solutions for a Simplified Shallow Elastic Fluids Model |
| title_full | Global Solutions for a Simplified Shallow Elastic Fluids Model |
| title_fullStr | Global Solutions for a Simplified Shallow Elastic Fluids Model |
| title_full_unstemmed | Global Solutions for a Simplified Shallow Elastic Fluids Model |
| title_short | Global Solutions for a Simplified Shallow Elastic Fluids Model |
| title_sort | global solutions for a simplified shallow elastic fluids model |
| url | http://dx.doi.org/10.1155/2014/920248 |
| work_keys_str_mv | AT yunguanglu globalsolutionsforasimplifiedshallowelasticfluidsmodel AT christianklingenberg globalsolutionsforasimplifiedshallowelasticfluidsmodel AT leonardorendon globalsolutionsforasimplifiedshallowelasticfluidsmodel AT deyinzheng globalsolutionsforasimplifiedshallowelasticfluidsmodel |