Damped wave equations on compact hyperbolic surfaces
Analysis of PDEs
2017-12-08 v1 Spectral Theory
Abstract
We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The proof is based on a similar strategy as in Dyatlov-Jin and in particular, uses the fractal uncertainty principle proved in Bourgain-Dyatlov.
Cite
@article{arxiv.1712.02692,
title = {Damped wave equations on compact hyperbolic surfaces},
author = {Long Jin},
journal= {arXiv preprint arXiv:1712.02692},
year = {2017}
}
Comments
23 pages