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PFDE with nonautonomous past

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

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