First-order hyperbolic pseudodifferential equations with generalized symbols
Analysis of PDEs
2007-05-23 v4 Functional Analysis
Abstract
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.
Cite
@article{arxiv.math/0307406,
title = {First-order hyperbolic pseudodifferential equations with generalized symbols},
author = {Guenther Hoermann},
journal= {arXiv preprint arXiv:math/0307406},
year = {2007}
}