PFDE with nonautonomous past

Simon Brendle; Rainer Nagel

doi:10.3934/dcds.2002.8.953

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2002, Volume 8, Issue 4: 953-966. Doi: 10.3934/dcds.2002.8.953

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PFDE with nonautonomous past

Simon Brendle^1, and
Rainer Nagel^2,

1.
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen
2.
University of Tübingen, Mathematics Institute, Auf der Morgenstelle 10, D-72076 Tübingen

Received: April 2001

Revised: February 2002

Published: October 2002

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 34K06, 35R10, 47D06.

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