On the wave equation with space dependent coefficients: singularities and lower order terms
Abstract
This paper complements the study of the wave equation with discontinuous coefficients initiated in 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 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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