Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms
Analysis of PDEs
2017-09-29 v1
Abstract
We investigate the long-time behavior 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.
Keywords
Cite
@article{arxiv.1709.09893,
title = {Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms},
author = {Martin Gugat and Vincent Perrollaz and Lionel Rosier},
journal= {arXiv preprint arXiv:1709.09893},
year = {2017}
}