Electron. J. Diff. Equ., Vol. 2012 (2012), No. 144, pp. 1-39.

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

Martina Glogowatz

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.

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Martina Glogowatz
Faculty of Mathematics
University of Vienna, Austria
email: martina.glogowatz@univie.ac.at

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