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A model hyperbolic partial differential equation with singular convolution operators and infinitely smooth solutions is studied. It is shown that short pulses, including finite-bandwidth pulses, propagate with a delay with respect to the wavefront. For a two-parameter family of such equations Green's functions are obtained in a simple self-similar form. As an application, it is demonstrated that the Gurevich-Lopatnikov dispersion law for a thin-layered porous medium can be approximated by a hyperbolic equation with singular memory.
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Hanyga et al. (2000) studied this question.
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