Geodesic
On solvability of parabolic functional differential equations in Banach spaces~(II)
Eurasian mathematical journal, Tome 11 (2020) no. 2, pp. 86-92

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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. 
@article{EMJ_2020_11_2_a8,
     author = {A. M. Selitskii},
     title = {On solvability of parabolic functional differential equations in {Banach} {spaces~(II)}},
     journal = {Eurasian mathematical journal},
     pages = {86--92},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2020_11_2_a8/}
}
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A. M. Selitskii. On solvability of parabolic functional differential equations in Banach spaces~(II). Eurasian mathematical journal, Tome 11 (2020) no. 2, pp. 86-92. http://geodesic.mathdoc.fr/item/EMJ_2020_11_2_a8/