On the limiting amplitude principle for the wave equation with variable coefficients
Analysis of PDEs
2024-04-08 v3 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
In this paper, we prove new results on the validity of the limiting amplitude principle (LAP) for the wave equation with nonconstant coefficients, not necessarily in divergence form. Under suitable assumptions on the coefficients and on the source term, we establish the LAP for space dimensions 2 and 3. This result is extended to one space dimension with an appropriate modification. We also quantify the LAP and thus provide estimates for the convergence of the time-domain solution to the frequency-domain solution. Our proofs are based on time-decay results of solutions of some auxiliary problems. The obtained results are illustrated numerically on radially symmetric problems in dimensions 1, 2 and 3.
Cite
@article{arxiv.2202.10105,
title = {On the limiting amplitude principle for the wave equation with variable coefficients},
author = {Anton Arnold and Sjoerd Geevers and Ilaria Perugia and Dmitry Ponomarev},
journal= {arXiv preprint arXiv:2202.10105},
year = {2024}
}