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Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms

Submission Status:epub ahead of print
  • We investigate the long-time behaviour of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not preserved, it is shown here that an exponential convergence towards the steady state still holds with a decay rate which is proportional to the logarithm of the amplitude of the source term. The result is stated for a system with dynamical boundary conditions in order to deal with initial data that are free of any compatibility condition. The proof of the existence and uniqueness of a solution defined for all positive times is also provided in this paper.

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Metadaten
Author:Martin Gugat, Lionel Rosier, Vincent Perrollaz
DOI:https://doi.org/10.1007/s00028-018-0449-z
Parent Title (English):Journal of Evolution Equations
Editor:W. Arendt, M. Pierre
Document Type:Article
Language:English
Date of Publication (online):2018/06/04
Date of first Publication:2018/06/05
Release Date:2018/06/05
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:C03
Licence (German):License LogoCreative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International