A note on local energy decay results for wave equations with a potential

2022/10/17 by Ryo Ikehata, Ikehata, Ryo
Engineering · Mathematics · #35B40 #35L05 #35L30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.08747

openalex publication_date 2022/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L²-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.

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