On solvability of parabolic functional differential equations in Banach spaces (II)

A. M. Selitskii<sup>ab

a</sup> Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 40 Vavilova St, 119333, Moscow, Russia
^b RUDN University, 6 Miklukho-Maklay St, 117198, Moscow, Russia

Abstract: In this paper, a parabolic functional differential equation is considered in the spaces $C(0, T; H^s_p (Q))$ for $s$ close to $1$ and $p$ close to $2$. The transformations of the space argument are supposed to be bounded in the spaces $H^s_p (Q)$ with small smoothness exponent and $p$ close to $2$. The corresponding resolvent estimate of the elliptic part of the operator is obtained in order to show that it generates a strongly continuous semigroup.

Keywords and phrases: functional differential equations, Lipschitz domain, Banach spaces.

MSC: 39A14

Received: 05.09.2018
Revised: 18.02.2020

Language: English

DOI: 10.32523/2077-9879-2020-11-2-86-92

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