Spectral stability of shock profiles for hyperbolically regularized systems of conservation laws
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917889232076800 |
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| author | Bärlin, Johannes |
| author_facet | Bärlin, Johannes |
| contents | We report a proof that under natural assumptions shock profiles viewed as heteroclinic travelling wave solutions to a hyperbolically regularized system of conservation laws are spectrally stable, if the shock amplitude is sufficiently small. This means that an associated Evans function $\mathcal{E}:Λ\rightarrow\mathbb{C}$ with $Λ\subset\mathbb{C}$ an open superset of the closed right half plane $\mathbb{H}^+\equiv\{κ\in\mathbb{C}:\text{Re}\,κ\geq 0\}$, has only one zero, namely a simple zero at $0$. The result is analogous to the one obtained in [FS02] and [PZ04] for parabolically regularized systems of conservation laws, and also distinctly extends findings on hyperbolic relaxation systems in [PZ04], [MZ09], [Ued09] . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12165 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectral stability of shock profiles for hyperbolically regularized systems of conservation laws Bärlin, Johannes Analysis of PDEs We report a proof that under natural assumptions shock profiles viewed as heteroclinic travelling wave solutions to a hyperbolically regularized system of conservation laws are spectrally stable, if the shock amplitude is sufficiently small. This means that an associated Evans function $\mathcal{E}:Λ\rightarrow\mathbb{C}$ with $Λ\subset\mathbb{C}$ an open superset of the closed right half plane $\mathbb{H}^+\equiv\{κ\in\mathbb{C}:\text{Re}\,κ\geq 0\}$, has only one zero, namely a simple zero at $0$. The result is analogous to the one obtained in [FS02] and [PZ04] for parabolically regularized systems of conservation laws, and also distinctly extends findings on hyperbolic relaxation systems in [PZ04], [MZ09], [Ued09] . |
| title | Spectral stability of shock profiles for hyperbolically regularized systems of conservation laws |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2208.12165 |