Discacciati, M, Garetto, C and Loizou, C (2022) On the wave equation with space dependent coefficients: singularities and lower order terms. [Preprint - Arxiv]
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.
Metadata
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| Institution: | The University of Leeds |
| Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > SWJTU Joint School (Leeds) |
| Depositing User: | Symplectic Publications |
| Date Deposited: | 28 Apr 2023 11:35 |
| Last Modified: | 28 Apr 2023 11:38 |
| Published Version: | https://arxiv.org/ |
| Identification Number: | https://doi.org/10.48550/arXiv.2208.03477 |
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