On the wave equation with space dependent coefficients: singularities and lower order terms
Analysis of PDEs
2022-08-09 v1
Abstract
This paper complements the study of the wave equation with discontinuous coefficients initiated in \cite{DGL:22} in the case of time-dependent coefficients. Here we assume that the equation coefficients are depending on space only and we formulate Levi conditions on the lower order terms to guarantee the existence of a very weak solution as defined in \cite{GR:14}. As a toy model we study the wave equation in conservative form with discontinuous velocity and we provide a qualitative analysis of the corresponding very weak solution via numerical methods.
Keywords
Cite
@article{arxiv.2208.03477,
title = {On the wave equation with space dependent coefficients: singularities and lower order terms},
author = {Marco Discacciati and Claudia Garetto and Costas Loizou},
journal= {arXiv preprint arXiv:2208.03477},
year = {2022}
}