Waves, structures, and the Riemann problem for a system of hyperbolic conservation laws
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915530847289344 |
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| author | Chugainova, A. P. Treschev, D. V. |
| author_facet | Chugainova, A. P. Treschev, D. V. |
| contents | A system of hyperbolic conservation laws $$ \partial_t u + \partial_x \partial_u Q = 0, \quad
Q = u_1^3 / 3 + u_1 u_2^2, \qquad
u = u(x,t) \in\mR^2, $$ as well as its viscous regularization $$
\partial_t u + \partial_x \partial_u Q = \calM \partial_x^2 u, \qquad
\calM = \diag (μ_1,μ_2), \quad μ_1>0,\, μ_2>0, $$ are studied. It is assumed that admissible shocks are those that satisfy the requirement of existence of a structure (the traveling wave criterion). A solution of the Riemann problem is constructed that consists of rarefaction waves and shocks with structure. Depending on the conditions imposed at $\pm\infty$, the solution also contains undercompressive shocks and Jouguet waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Waves, structures, and the Riemann problem for a system of hyperbolic conservation laws Chugainova, A. P. Treschev, D. V. Mathematical Physics 35L67, 34C99, 35B35, 35L65 A system of hyperbolic conservation laws $$ \partial_t u + \partial_x \partial_u Q = 0, \quad Q = u_1^3 / 3 + u_1 u_2^2, \qquad u = u(x,t) \in\mR^2, $$ as well as its viscous regularization $$ \partial_t u + \partial_x \partial_u Q = \calM \partial_x^2 u, \qquad \calM = \diag (μ_1,μ_2), \quad μ_1>0,\, μ_2>0, $$ are studied. It is assumed that admissible shocks are those that satisfy the requirement of existence of a structure (the traveling wave criterion). A solution of the Riemann problem is constructed that consists of rarefaction waves and shocks with structure. Depending on the conditions imposed at $\pm\infty$, the solution also contains undercompressive shocks and Jouguet waves. |
| title | Waves, structures, and the Riemann problem for a system of hyperbolic conservation laws |
| topic | Mathematical Physics 35L67, 34C99, 35B35, 35L65 |
| url | https://arxiv.org/abs/2510.02070 |