%0 Journal Article
%T Factorization of second-order strictly hyperbolic operators with non-smooth coefficients and microlocal diagonalization
%A Martina Glogowatz
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X We study strictly hyperbolic partial differential operators of second-order with non-smooth coefficients. After modeling 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.
%K Algebras of generalized functions
%K wave front sets
%K parameter dependent pseudodifferential operators
%U http://ejde.math.txstate.edu/Volumes/2012/144/abstr.html