Nonautonomous retarded wave equations (Q5955570)

In the present paper the authors study the existence and uniqueness of \(C^2\) solutions to nonautonomous retarded wave equations with memory effects. To this end the authors first tackle the well-posedness problem for a class of Volterra nonautonomous retarded differential equations in a Banach space. The main tools in the proofs are the Hille-Yosida operator theory, the extrapolation theory for Hille-Yosida operators, and a result on nonautonomous perturbations due to Desch-Schnappacher.