Electron. J. Differential Equations,
Vol. 2018 (2018), No. 42, pp. 149.
Factorization of secondorder strictly hyperbolic operators with logarithmic
slow scale coefficients and generalized microlocal approximations
Martina Glogowatz
Abstract:
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 firstorder 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 oneway wave equations where a dissipative term is added
to suppress singularities outside the given domain. We obtain wellposedness
of the corresponding Cauchy problem for the approximated oneway wave equation
with a dissipative term.
Submitted January 24, 2017. Published February 6, 2018.
Math Subject Classifications: 35S05, 46F30.
Key Words: Hyperbolic equations and systems; algebras of generalized functions.
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Martina Glogowatz
Faculty of Mathematics
University of Vienna, Austria
email: martina.glogowatz@univie.ac.at

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