Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations
Texas State University, Department of Mathematics
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.
Hyperbolic equations and systems, Algebras of generalized functions
Glogowatz, 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.
Attribution 4.0 International