Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms
- 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.
Author: | Martin Gugat, Lionel Rosier, Vincent Perrollaz |
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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): | Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International |