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Inhomogeneous wave equation with t-dependent singular coefficients

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posted on 2022-02-18, 10:00 authored by Marco DiscacciatiMarco Discacciati, Claudia Garetto, Costas Loizou
This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are formulated in order to obtain a very weak solution as introduced in [GR14]. Very weak solutions for this kind of equations are also investigated from a numerical point of view in two toy models: the wave equation with a Heaviside function and a delta distribution, respectively, as coefficient in its principal part.

Funding

Hyperbolic problems with discontinuous coefficients

Engineering and Physical Sciences Research Council

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History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Differential Equations

Volume

319

Pages

131 - 185

Publisher

Elsevier

Version

  • AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Journal of Differential Equations and the definitive published version is available at https://doi.org/10.1016/j.jde.2022.02.039.

Acceptance date

2022-02-15

Publication date

2022-03-02

Copyright date

2022

ISSN

0022-0396

Language

  • en

Depositor

Dr Marco Discacciati. Deposit date: 17 February 2022

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