We consider the wave equations with perturbation of the first order differential operators, the coeffcients of which depend on both the space and time variables. Under suitable conditions on the coeffcients, we show the existence of the scattering operator. The main tool used is space-time energy estimates of solutions.
"On Scattering for Wave Equations with Time Dependent Coefficients." Tsukuba J. Math. 31 (2) 327 - 342, December 2007. https://doi.org/10.21099/tkbjm/1496165152