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
Item Type: | Preprint |
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Authors/Creators: |
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Dates: |
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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: | 10.48550/arXiv.2208.03477 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198287 |