A note on local energy decay results for wave equations with a potential
Analysis of PDEs
2022-10-19 v2
Abstract
In this paper we consider the local energy decay result for wave equations with a short-range potential. It is important to note that one never uses a finite speed of propagation property unlike the historical previous papers. The essential parts of analysis are in getting L^2-bound of the solution itself, and deriving the weighted energy estimates. In this paper we only use a simple multiplier method to treat the variable coefficient case, and do not rely on any resolvent estimates.
Keywords
Cite
@article{arxiv.2210.08747,
title = {A note on local energy decay results for wave equations with a potential},
author = {Ryo Ikehata},
journal= {arXiv preprint arXiv:2210.08747},
year = {2022}
}
Comments
9 pages. Several typos in the former version (v1) are improved