On the Gelfand Problem and Viscosity Matrices for Two-Dimensional Hyperbolic Systems of Conservation Laws
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914787241230336 |
|---|---|
| author | Chu, Shaoshuai Kliakhandler, Igor Kurganov, Alexander |
| author_facet | Chu, Shaoshuai Kliakhandler, Igor Kurganov, Alexander |
| contents | We present counter-intuitive examples of a viscous regularizations of a two-dimensional strictly hyperbolic system of conservation laws. The regularizations are obtained using two different viscosity matrices. While for both of the constructed ``viscous'' systems waves propagating in either $x$- or $y$-directions are stable, oblique waves may be linearly unstable. Numerical simulations fully corroborate these analytical results. To the best of our knowledge, this is the first nontrivial result related to the multidimensional Gelfand problem. Our conjectures provide direct answer to Gelfand's problem both in one- and multi-dimensional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Gelfand Problem and Viscosity Matrices for Two-Dimensional Hyperbolic Systems of Conservation Laws Chu, Shaoshuai Kliakhandler, Igor Kurganov, Alexander Numerical Analysis We present counter-intuitive examples of a viscous regularizations of a two-dimensional strictly hyperbolic system of conservation laws. The regularizations are obtained using two different viscosity matrices. While for both of the constructed ``viscous'' systems waves propagating in either $x$- or $y$-directions are stable, oblique waves may be linearly unstable. Numerical simulations fully corroborate these analytical results. To the best of our knowledge, this is the first nontrivial result related to the multidimensional Gelfand problem. Our conjectures provide direct answer to Gelfand's problem both in one- and multi-dimensional cases. |
| title | On the Gelfand Problem and Viscosity Matrices for Two-Dimensional Hyperbolic Systems of Conservation Laws |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.04214 |