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

Martina Glogowatz

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arXiv · 1112.5615

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

Martina Glogowatz

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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.

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Martina Glogowatz. 2011-12-23. Factorization of Second-order strictly hyperbolic operators with non-smooth coefficients and microlocal diagonalization. https://arxiv.org/abs/1112.5615

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