Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping
Abstract This paper is focused on the Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The genera...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-11-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-023-01798-z |
| _version_ | 1827709355486609408 |
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| author | Shiwei Li |
| author_facet | Shiwei Li |
| author_sort | Shiwei Li |
| collection | DOAJ |
| description | Abstract This paper is focused on the Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing viscosity method proves the existence, uniqueness, and stability of non-self-similar solutions. |
| first_indexed | 2024-03-10T17:19:47Z |
| format | Article |
| id | doaj.art-f1b92cc104eb4461a7b473e5bb7e116d |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-10T17:19:47Z |
| publishDate | 2023-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-f1b92cc104eb4461a7b473e5bb7e116d2023-11-20T10:23:12ZengSpringerOpenBoundary Value Problems1687-27702023-11-012023112010.1186/s13661-023-01798-zRiemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate dampingShiwei Li0College of science, Henan University of EngineeringAbstract This paper is focused on the Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing viscosity method proves the existence, uniqueness, and stability of non-self-similar solutions.https://doi.org/10.1186/s13661-023-01798-zConservation lawsTime-gradually-degenerate dampingDelta-shocksVanishing viscosity method |
| spellingShingle | Shiwei Li Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping Boundary Value Problems Conservation laws Time-gradually-degenerate damping Delta-shocks Vanishing viscosity method |
| title | Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping |
| title_full | Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping |
| title_fullStr | Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping |
| title_full_unstemmed | Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping |
| title_short | Riemann problem for a 2 × 2 $2\times 2$ hyperbolic system with time-gradually-degenerate damping |
| title_sort | riemann problem for a 2 2 2 times 2 hyperbolic system with time gradually degenerate damping |
| topic | Conservation laws Time-gradually-degenerate damping Delta-shocks Vanishing viscosity method |
| url | https://doi.org/10.1186/s13661-023-01798-z |
| work_keys_str_mv | AT shiweili riemannproblemfora222times2hyperbolicsystemwithtimegraduallydegeneratedamping |