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Short communications

On the solvability of parabolic functional differential equations in Banach spaces

A. M. Selitskii<sup>ab

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

Abstract: In this paper, a parabolic functional differential equation is considered in the spaces $C(0,T;H_p^1(Q))$ for $p$ close to $2$. The transformations of the space argument are supposed to be multiplicators of the Sobolev spaces with a small smoothness exponent. The machinery of the investigation is based on the semigroup theory. In particular, it is proved that the elliptic part of the operator is a generator of a strongly continuous semigroup.

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

MSC: 39A14

Received: 10.06.2016

Language: English

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