First-order hyperbolic pseudodifferential equations with generalized symbols

Details First-order hyperbolic pseudodifferential equations with generalized symbols First-order hyperbolic pseudodifferential equations with generalized symbols

2003-07-31

arxiv.org/abs/math/0307406v4

Mathematics

Analysis of PDEs

Scientific paper

We consider the Cauchy problem for a hyperbolic pseudodifferential operator whose symbol is generalized, resembling a representative of a Colombeau generalized function. Such equations arise, for example, after a reduction-decoupling of second-order model systems of differential equations in seismology. We prove existence of a unique generalized solution under log-type growth conditions on the symbol, thereby extending known results for the case of differential operators with generalized functions as coefficients.

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