Inhomogeneous wave equation with $t$-dependent singular coefficients

Claudia Garetto; Costas Loizou; Marci Discacciati

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Inhomogeneous wave equation with t-dependent singular coefficients

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arxiv 2111.11149 v1 pith:NTQLXRIJ submitted 2021-11-22 math.AP

Inhomogeneous wave equation with t-dependent singular coefficients

Marci Discacciati , Claudia Garetto , Costas Loizou This is my paper

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keywords equationwavecoefficientsdependentinhomogeneousordersingularvery

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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.

Inhomogeneous wave equation with t-dependent singular coefficients

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