Abstract and Applied Analysis
Volume 2003 (2003), Issue 16, Pages 933-951
doi:10.1155/S1085337503306335

A spectral mapping theorem for semigroups solving PDEs with nonautonomous past

Abstract

We prove a spectral mapping theorem for semigroups solving partial differential equations with nonautonomous past. This theorem is then used to give spectral conditions for the stability of the solutions of the equations.