Spectral stability of shock profiles for hyperbolically regularized systems of conservation laws

2022/08/25 by Johannes Bärlin, Bärlin, Johannes · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2208.12165

openalex publication_date 2022/08/25 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28

Abstract

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 E:Λ→ℂ with Λ⊂ℂ an open superset of the closed right half plane ℍ⁺≡\κ∈ℂ:Re κ≥ 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] .

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