Electron. J. Differential Equations, Vol. 2018 (2018), No. 42, pp. 1-49.

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

Martina Glogowatz

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.

Show me the PDF file (529 KB), TEX file for this article.

Martina Glogowatz
Faculty of Mathematics
University of Vienna, Austria
email: martina.glogowatz@univie.ac.at

Return to the EJDE web page