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Pseudo-Differential Operators, Generalized Functions and Asymptotics
This paper is devoted to the investigation of propagation of singularities in hyperbolic equations with non-smooth coefficients, using the Colombeau theory of generalized functions. As a model problem, we study the Cauchy problem for the one-dimensional wave equation with a discontinuous coefficient depending on time. After demonstrating the existence and uniqueness of generalized solutions in the sense of Colombeau to the problem, we investigate the phenomenon of propagation of singularities,doi:10.1007/978-3-0348-0585-8_18 fatcat:qpvcg2li5vahxhtvcvcrj2cqie