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November  2002, 8(4): 953-966. doi: 10.3934/dcds.2002.8.953

PFDE with nonautonomous past

Simon Brendle 1, and  Rainer Nagel 2,

1. 

Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
2. 

University of Tübingen, Mathematics Institute, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Received  April 2001 Revised  February 2002 Published  July 2002

We study Cauchy problems associated to partial differential equations with infinite delay where the history function is modified by an evolution family. Using sophisticated tools from semigroup theory such as evolution semigroups, extrapolation spaces, or the critical spectrum, we prove well-posedness and characterize the asymptotic behavior of the solution semigroup by an operator-valued characteristic equation.
Keywords: nonautonomous Cauchy problem, evolution semigroups, stability., pde with delay.
Mathematics Subject Classification: 34K06, 35R10, 47D0.
Citation: Simon Brendle, Rainer Nagel. PFDE with nonautonomous past. Discrete & Continuous Dynamical Systems, 2002, 8 (4) : 953-966. doi: 10.3934/dcds.2002.8.953
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