Factorization of second-order strictly hyperbolic operators with logarithmic slow scale coefficients and generalized microlocal approximations
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2018-02-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/42/abstr.html |
| Summary: | 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. |
|---|---|
| ISSN: | 1072-6691 |