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Boundary stabilization of multi-dimensional first-order quasilinear hyperbolic systems
Abstract
We study the long-time behaviour of multi-dimensional first-order symmetrizable quasilinear hyperbolic systems with nonlinear feedback boundary conditions. Assuming strict interior and boundary Lyapunov inequalities for the linearized system and non-characteristic boundaries, we prove global existence for small initial data and exponential H^s decay, with s>d/2+1 an integer. We consider both bounded smooth domains and flat periodic cylinders, and illustrate the results with physical examples and numerical simulations.
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BibTeX
@misc{yang2026boundary,
title = {{Boundary stabilization of multi-dimensional first-order quasilinear hyperbolic systems}},
author = {Haitian Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13577},
eprint = {2610.13577},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13577},
}
RIS
TY - UNPB
TI - Boundary stabilization of multi-dimensional first-order quasilinear hyperbolic systems
AU - Haitian Yang
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13577
UR - https://arxiv.org/abs/2610.13577
AB - We study the long-time behaviour of multi-dimensional first-order symmetrizable quasilinear hyperbolic systems with nonlinear feedback boundary conditions. Assuming strict interior and boundary Lyapunov inequalities for the linearized system and non-characteristic boundaries, we prove global existence for small initial data and exponential H^s decay, with s>d/2+1 an integer. We consider both bounded smooth domains and flat periodic cylinders, and illustrate the results with physical examples and numerical simulations.
ER -