Discacciati, M., Garetto, C. orcid.org/0000-0001-7907-6072 and Loizou, C. (2023) On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order Terms. Acta Applicandae Mathematicae, 187 (1). 10. ISSN 0167-8019
Abstract
This paper complements the study of the wave equation with discontinuous coefficients initiated in (Discacciati et al. in J. Differ. Equ. 319 (2022) 131–185) 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 (Garetto and Ruzhansky in Arch. Ration. Mech. Anal. 217 (2015) 113–154). 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: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Hyperbolic equations; Very weak solutions; Regularisation |
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: | 19 Sep 2023 14:40 |
Last Modified: | 19 Sep 2023 14:40 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10440-023-00601-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:203482 |