Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 144, pp. 139.
Factorization of secondorder strictly hyperbolic operators with
nonsmooth coefficients and microlocal diagonalization
Martina Glogowatz
Abstract:
We study strictly hyperbolic partial differential operators of secondorder
with nonsmooth coefficients. After modeling them as semiclassical Colombeau
equations of logtype we provide a factorization procedure on some
timespacefrequency domain. As a result the operator is written as a
product of two semiclassical firstorder constituents of logtype 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
firstorder 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.
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Martina Glogowatz
Faculty of Mathematics
University of Vienna, Austria
email: martina.glogowatz@univie.ac.at

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