Glogowatz, Martina2022-01-072022-01-072018-02-06Glogowatz, M. (2018). Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations. <i>Electronic Journal of Differential Equations, 2018</i>(42), pp. 1-49.1072-6691https://hdl.handle.net/10877/15098We 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.Text49 pages1 file (.pdf)enAttribution 4.0 InternationalHyperbolic equations and systemsAlgebras of generalized functionsArticle