. A P ] 1 1 A ug 2 00 3 FIRST - ORDER HYPERBOLIC PSEUDODIFFERENTIAL EQUATIONS WITH GENERALIZED SYMBOLS
نویسنده
چکیده
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 logtype growth conditions on the symbol, thereby extending known results for the case of differential operators ([17, 19]).
منابع مشابه
First-order Hyperbolic Pseudodifferential Equations with Generalized Symbols
We consider the Cauchy problem for a hyperbolic pseudodifferential operator whose symbol is 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 ...
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