Basic Theory for Generalized Linear Solid Viscoelastic Models

In this paper, we consider the generalized linear solid model of viscoelastic wave propagation, which is modeled by a system of integro-differential equations. We show the existence and uniqueness of a weak solution to the initial-boundary value problem; we show that the solution has finite propagation speed; and we prove regularity results for the solution, depending on the regularity of the domain, the material parameters, the initial data, and the source function.