Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients

Abstract

Fractional wave equations with time-dependent coefficients are natural generations of classical wave equations which can be used to characterize propagation of wave in inhomogeneous media with frequency-dependent power-law behavior. This paper discusses the well-posedness and regularity results of the weak solution for a fractional wave equation allowing that the coefficients may have low regularity. Our analysis relies on mollification arguments, Galerkin methods, and energy arguments.