Factorization of Second-order strictly hyperbolic operators with non-smooth coefficients and microlocal diagonalization
Analysis of PDEs
2011-12-26 v1
Abstract
We study strictly hyperbolic partial differential operators of second order with non-smooth coefficients. After modelling them as semiclassical Colombeau equations of log-type we provide a factorization procedure on some time-space-frequency domain. As a result the operator is written as a product of two semiclassical first-order constituents of log-type which approximates the modelled operator microlocally at infinite points. We then present a diagonalization method so that microlocally at infinity the governing equation is equal to a coupled system of two semiclassical first-order strictly hyperbolic pseudodifferential equations. Furthermore we compute the coupling effect. We close with some remarks on the results and future directions.
Cite
@article{arxiv.1112.5615,
title = {Factorization of Second-order strictly hyperbolic operators with non-smooth coefficients and microlocal diagonalization},
author = {Martina Glogowatz},
journal= {arXiv preprint arXiv:1112.5615},
year = {2011}
}