Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917002953621504 |
|---|---|
| author | Sroczinski, Matthias Zumbrun, Kevin |
| author_facet | Sroczinski, Matthias Zumbrun, Kevin |
| contents | We give the first proof of nonlinear stability for smooth shock profiles of second-order dissipative hyperbolic-hyperbolic systems under the assumption of spectral stability, showing stability of smooth small-amplitude profiles in dimensions greater than or equal to two. This class of systems notably includes the two types of causal viscous relativistic gas models introduced respectively by Freistühler-Temple and Bemfica-Disconzi-Noronha, and (the equivalent second-order form of) a class of first-order numerical relaxation systems generalizing the well-known Jin-Xin relaxation schemes. A significant technical innovation is a new para-differential type of nonlinear damping estimate similar to that used by the first author to study stability of constant states, allowing the treatment of systems far from the symmetric structure required for the standard ``Kawashima-type'' energy estimates that are typically used for that purpose. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems Sroczinski, Matthias Zumbrun, Kevin Analysis of PDEs We give the first proof of nonlinear stability for smooth shock profiles of second-order dissipative hyperbolic-hyperbolic systems under the assumption of spectral stability, showing stability of smooth small-amplitude profiles in dimensions greater than or equal to two. This class of systems notably includes the two types of causal viscous relativistic gas models introduced respectively by Freistühler-Temple and Bemfica-Disconzi-Noronha, and (the equivalent second-order form of) a class of first-order numerical relaxation systems generalizing the well-known Jin-Xin relaxation schemes. A significant technical innovation is a new para-differential type of nonlinear damping estimate similar to that used by the first author to study stability of constant states, allowing the treatment of systems far from the symmetric structure required for the standard ``Kawashima-type'' energy estimates that are typically used for that purpose. |
| title | Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.09287 |