Self‐similar viscosity approach to the Riemann problem for a strictly hyperbolic system of conservation laws
Here, we study the Riemann problem for a strictly hyperbolic system of conservation laws, which occurs in gas dynamics and nonlinear elasticity. We establish the existence and uniqueness of the solution of Riemann problem containing delta shock wave by employing self‐similar vanishing viscosity appr...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2023-04, Vol.46 (6), p.7265-7284 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Chhatria, Balakrishna Sen, Anupam Raja Sekhar, T. |
| description | Here, we study the Riemann problem for a strictly hyperbolic system of conservation laws, which occurs in gas dynamics and nonlinear elasticity. We establish the existence and uniqueness of the solution of Riemann problem containing delta shock wave by employing self‐similar vanishing viscosity approach. We prove that delta shock is stable under self‐similar viscosity perturbation, which ensures that delta shock wave is a unique entropy solution. |
| doi_str_mv | 10.1002/mma.8969 |
| format | Article |
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| ispartof | Mathematical methods in the applied sciences, 2023-04, Vol.46 (6), p.7265-7284 |
| issn | 0170-4214 1099-1476 |
| language | eng |
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| source | Wiley-Blackwell Journals |
| subjects | Cauchy problems Conservation laws delta shock wave Entropy of solution Gas dynamics Hyperbolic systems Nonlinear dynamics Perturbation Riemann problem self‐similar vanishing viscosity strictly hyperbolic system Viscosity |
| title | Self‐similar viscosity approach to the Riemann problem for a strictly hyperbolic system of conservation laws |
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