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/

[1] M. S. Agranovich, Sobolev spaces, their generalizations, and elliptic problems in smooth and Lipschitz domains, Springer, Heidelberg–New York, 2015 | MR | Zbl

[2] M. S. Agranovich, “Spectral problems in Sobolev-type spaces for strongly elliptic systems in Lipschitz domains”, Math. Nachr., 289:16 (2016), 1968–1988 | DOI | MR

[3] A. Ashyralyev, P. E. Sobolevskii, Well-posedness of parabolic difference equations, Birkhauser, Basel, 1994 | MR

[4] R. Dautray, J.-L. Lions, Analyse mathématique et calcul numérique, v. 3, Masson, Paris, 1985

[5] E. M. Ouhabaz, Analysis of heat equations on domains, Princeton Univ. Press, Princeton–Oxford, 2005 | MR | Zbl

[6] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer, Berlin–Heidelberg, 1983 | MR | Zbl

[7] V. S. Rychkov, “On restrictions and extensions of the Besov and Tribel-Lizorkin spaces with respect to Lipschitz domains”, J. London Math. Soc., 60:2 (1997), 237–257 | MR

[8] A. M. Selitskii, “Space of initial data for the second boundary-value problem for a parabolic differential-difference equation in Lipschitz domains”, Math. Notes, 94:3 (2013), 135–138 | MR

[9] A. M. Selitskii, “The space of initial data of the Robin boundary-value problem for parabolic differential-difference equations”, Contemporary Analysis and Applied Mathematics, 1:2 (2013), 91–97 | MR | Zbl

[10] A. M. Selitskii, A. L. Skubachevskii, “The second boundary-value problem for parabolic differential-difference equations”, J. Math. Sci., 143:4 (2007), 3386–3400 | DOI | MR

[11] A. L. Skubachevskii, “Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics”, Nonlinear Anal., 32:2 (1998), 261–278 | DOI | MR | Zbl

[12] H. Triebel, Interpolation theory, function spaces, differential operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978 | MR