On the wave equation with space dependent coefficients: singularities and lower order terms

Claudia Garetto; Costas Loizou; Marco Discacciati

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On the wave equation with space dependent coefficients: singularities and lower order terms

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arxiv 2208.03477 v1 pith:KXDK4DJ4 submitted 2022-08-06 math.AP

Marco Discacciati , Claudia Garetto , Costas Loizou This is my paper · ORCID

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keywords coefficientsequationwavecitediscontinuouslowerordersolution

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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.

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