Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations

Date

2018-02-06

Authors

Glogowatz, Martina

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

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 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.

Description

Keywords

Hyperbolic equations and systems, Algebras of generalized functions

Citation

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.

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Attribution 4.0 International

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