Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 144, pp. 1-39.

Title: Factorization of second-order strictly hyperbolic operators with
       non-smooth coefficients and microlocal diagonalization

Author: Martina Glogowatz (Univ. of Vienna, Austria)

Abstract:
 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.

Submitted November 8, 2011. Published August 21, 2012.
Math Subject Classifications: 35S05, 46F30.
Key Words: Algebras of generalized functions; wave front sets;
           parameter dependent pseudodifferential operators.