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arXiv · 2208.03477

On the wave equation with space dependent coefficients: singularities and lower order terms

Marco Discacciati·Claudia Garetto·Costas Loizou
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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.

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Marco Discacciati, Claudia Garetto, Costas Loizou. 2022-08-06. On the wave equation with space dependent coefficients: singularities and lower order terms. https://arxiv.org/abs/2208.03477

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