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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