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.
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
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