Factorization of second-order strictly hyperbolic operators with non-smooth coefficients and microlocal diagonalization
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 produc...
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| Format: | Article |
| Language: | English |
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Texas State University
2012-08-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/144/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |