Inhomogeneous wave equation with $t$-dependent singular coefficients
Analysis of PDEs
2021-11-23 v1
Abstract
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 \cite{GR:14}. 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.
Keywords
Cite
@article{arxiv.2111.11149,
title = {Inhomogeneous wave equation with $t$-dependent singular coefficients},
author = {Marci Discacciati and Claudia Garetto and Costas Loizou},
journal= {arXiv preprint arXiv:2111.11149},
year = {2021}
}