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On the evolution operator for abstract parabolic equations

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Abstract

We find a new construction of the evolution operatorG(t, s) associated to a family {A(t), 0≦t≦T} of generators of analytic semigroups in a Banach spaceX. We study the dependence ofG (t, s) ont ands, and we give regularity results for the solution of the i.v.p.u′(t)=A(t)u(t)+f(t),u(0)=x.

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  1. Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56100, Pisa, Italy

    Alessandra Lunardi

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  1. Alessandra Lunardi
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Lunardi, A. On the evolution operator for abstract parabolic equations. Israel J. Math. 60, 281–314 (1987). https://doi.org/10.1007/BF02780395

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  • DOI: https://doi.org/10.1007/BF02780395

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