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EXPONENTIAL ASYMPTOTIC STABILITY OF RIEMANN SHOCKS OF HYPERBOLIC SYSTEMS OF BALANCE LAWS

Abstract : For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital stability. As a preparation, we also prove similar results for constant solutions of initial value and initial boundary value problems, that seem to be new in this generality. Main key technical ingredients include the design of a nonlinear change of variables providing a hypocoercive Kawashima-type structure with dissipative boundary conditions in the high-frequency regime and the explicit identification of most singular parts of the linearized evolution, both being deduced from the mere spectral assumption.
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https://hal.archives-ouvertes.fr/hal-03738369
Contributor : Grégory Faye Connect in order to contact the contributor
Submitted on : Tuesday, July 26, 2022 - 9:44:21 AM
Last modification on : Wednesday, August 3, 2022 - 3:49:58 AM

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  • HAL Id : hal-03738369, version 1

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Grégory Faye, L. Miguel Rodrigues. EXPONENTIAL ASYMPTOTIC STABILITY OF RIEMANN SHOCKS OF HYPERBOLIC SYSTEMS OF BALANCE LAWS. 2022. ⟨hal-03738369⟩

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