Stochastic perturbation and zero noise limit for scalar conservation laws
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911238869483520 |
|---|---|
| author | Fjordholm, Ulrik S. Ørke, Magnus C. |
| author_facet | Fjordholm, Ulrik S. Ørke, Magnus C. |
| contents | Scalar conservation laws sit at the intersection between being simple enough to study analytically, while being complex enough to exhibit a wide range of nonlinear phenomena. We introduce a novel stochastic perturbation of scalar conservation laws, inspired by mean field games. We prove well-posedness of the stochastically perturbed equation; prove that it converges as the noise parameter is sent to $0$; and that the limit is the unique entropy solution of the conservation law. Thus, the noise acts as a selection criterion for (deterministic) conservation laws. This is the first such result for nonlinear hyperbolic conservation laws. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic perturbation and zero noise limit for scalar conservation laws Fjordholm, Ulrik S. Ørke, Magnus C. Analysis of PDEs 60H50, 35L65, 60H15 Scalar conservation laws sit at the intersection between being simple enough to study analytically, while being complex enough to exhibit a wide range of nonlinear phenomena. We introduce a novel stochastic perturbation of scalar conservation laws, inspired by mean field games. We prove well-posedness of the stochastically perturbed equation; prove that it converges as the noise parameter is sent to $0$; and that the limit is the unique entropy solution of the conservation law. Thus, the noise acts as a selection criterion for (deterministic) conservation laws. This is the first such result for nonlinear hyperbolic conservation laws. |
| title | Stochastic perturbation and zero noise limit for scalar conservation laws |
| topic | Analysis of PDEs 60H50, 35L65, 60H15 |
| url | https://arxiv.org/abs/2510.24475 |