Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations
We give a factorization procedure for a strictly hyperbolic partial differential operator of second order with logarithmic slow scale coefficients. From this we can microlocally diagonalize the full wave operator which results in a coupled system of two first-order pseudodifferential equations in...
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| Format: | Article |
| Language: | English |
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Texas State University
2018-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/42/abstr.html |
| _version_ | 1818020227442540544 |
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| author | Martina Glogowatz |
| author_facet | Martina Glogowatz |
| author_sort | Martina Glogowatz |
| collection | DOAJ |
| description | We give a factorization procedure for a strictly hyperbolic partial differential
operator of second order with logarithmic slow scale coefficients.
From this we can microlocally diagonalize the full wave operator which results
in a coupled system of two first-order pseudodifferential equations in a
microlocal sense. Under the assumption that the full wave equation is
microlocal regular in a fixed domain of the phase space, we can approximate
the problem by two one-way wave equations where a dissipative term is added
to suppress singularities outside the given domain. We obtain well-posedness
of the corresponding Cauchy problem for the approximated one-way wave equation
with a dissipative term. |
| first_indexed | 2024-04-14T08:03:11Z |
| format | Article |
| id | doaj.art-48475ef9aae44bd7ba0452e20dcc6764 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-14T08:03:11Z |
| publishDate | 2018-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-48475ef9aae44bd7ba0452e20dcc67642022-12-22T02:04:50ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-02-01201842,149Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximationsMartina Glogowatz0 Univ. of Vienna, Austria We give a factorization procedure for a strictly hyperbolic partial differential operator of second order with logarithmic slow scale coefficients. From this we can microlocally diagonalize the full wave operator which results in a coupled system of two first-order pseudodifferential equations in a microlocal sense. Under the assumption that the full wave equation is microlocal regular in a fixed domain of the phase space, we can approximate the problem by two one-way wave equations where a dissipative term is added to suppress singularities outside the given domain. We obtain well-posedness of the corresponding Cauchy problem for the approximated one-way wave equation with a dissipative term.http://ejde.math.txstate.edu/Volumes/2018/42/abstr.htmlHyperbolic equations and systemsalgebras of generalized functions |
| spellingShingle | Martina Glogowatz Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations Electronic Journal of Differential Equations Hyperbolic equations and systems algebras of generalized functions |
| title | Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations |
| title_full | Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations |
| title_fullStr | Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations |
| title_full_unstemmed | Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations |
| title_short | Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations |
| title_sort | factorization of second order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations |
| topic | Hyperbolic equations and systems algebras of generalized functions |
| url | http://ejde.math.txstate.edu/Volumes/2018/42/abstr.html |
| work_keys_str_mv | AT martinaglogowatz factorizationofsecondorderstrictlyhyperbolicoperatorswithlogarithmicslowscalecoefficientsandgeneralizedmicrolocalapproximations |