Geodesic
On the solvability of parabolic functional differential equations in~Banach spaces
Eurasian mathematical journal, Tome 7 (2016) no. 4, pp. 85-91

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{EMJ_2016_7_4_a5,
     author = {A. M. Selitskii},
     title = {On the solvability of parabolic functional differential equations {in~Banach} spaces},
     journal = {Eurasian mathematical journal},
     pages = {85--91},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2016_7_4_a5/}
}
TY  - JOUR
AU  - A. M. Selitskii
TI  - On the solvability of parabolic functional differential equations in~Banach spaces
JO  - Eurasian mathematical journal
PY  - 2016
SP  - 85
EP  - 91
VL  - 7
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2016_7_4_a5/
LA  - en
ID  - EMJ_2016_7_4_a5
ER  - 
%0 Journal Article
%A A. M. Selitskii
%T On the solvability of parabolic functional differential equations in~Banach spaces
%J Eurasian mathematical journal
%D 2016
%P 85-91
%V 7
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2016_7_4_a5/
%G en
%F EMJ_2016_7_4_a5
A. M. Selitskii. On the solvability of parabolic functional differential equations in~Banach spaces. Eurasian mathematical journal, Tome 7 (2016) no. 4, pp. 85-91. http://geodesic.mathdoc.fr/item/EMJ_2016_7_4_a5/