Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type
This paper is devoted to the study of delta shock waves for a hyperbolic system of conservation laws of Keyfitz-Kranzer type with two linearly degenerate characteristics. The Riemann problem is solved constructively. The Riemann solutions include exactly two kinds. One consists of two (or just one)...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/958120 |
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| author | Hongjun Cheng |
| author_facet | Hongjun Cheng |
| author_sort | Hongjun Cheng |
| collection | DOAJ |
| description | This paper is devoted to the study of delta shock waves for a hyperbolic system of conservation laws of Keyfitz-Kranzer type with two linearly degenerate characteristics. The Riemann problem is solved constructively. The Riemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solution are established. These analytical results match well the numerical ones. Finally, two kinds of interactions of elementary waves are discussed. |
| format | Article |
| id | doaj-art-e3c3ba24ef5d46249fe39bc72046b941 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e3c3ba24ef5d46249fe39bc72046b9412025-02-03T01:04:04ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/958120958120Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer TypeHongjun Cheng0School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, ChinaThis paper is devoted to the study of delta shock waves for a hyperbolic system of conservation laws of Keyfitz-Kranzer type with two linearly degenerate characteristics. The Riemann problem is solved constructively. The Riemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solution are established. These analytical results match well the numerical ones. Finally, two kinds of interactions of elementary waves are discussed.http://dx.doi.org/10.1155/2013/958120 |
| spellingShingle | Hongjun Cheng Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type Advances in Mathematical Physics |
| title | Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type |
| title_full | Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type |
| title_fullStr | Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type |
| title_full_unstemmed | Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type |
| title_short | Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type |
| title_sort | delta shock waves for a linearly degenerate hyperbolic system of conservation laws of keyfitz kranzer type |
| url | http://dx.doi.org/10.1155/2013/958120 |
| work_keys_str_mv | AT hongjuncheng deltashockwavesforalinearlydegeneratehyperbolicsystemofconservationlawsofkeyfitzkranzertype |