Abstract and Applied Analysis
Volume 2003 (2003), Issue 16, Pages 933-951

A spectral mapping theorem for semigroups solving PDEs with nonautonomous past

Genni Fragnelli

Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, via della Ricerca Scientifica, Roma 00133, Italy

Received 20 June 2002

Copyright © 2003 Genni Fragnelli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.