A characterization of well‐posedness for the second order abstract Cauchy problems with finite delay

Seyedeh Marzieh Ghavidel

Mathematische Nachrichten, 2023, vol. 296, issue 6, 2352-2365

Abstract: In this work, we introduce a strongly continuous one‐parameter family of bounded linear operators that completely describes the well‐posedness of a second order abstract differential delay equation in the initial history space Lp([−r,0];X)$L^p([-r,0];X)$, r>0$r>0$. This family, which satisfies a specific functional equation is applied to characterize the mild solution of the considered second order delay equation.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:6:p:2352-2365

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