The Space of Initial Data of the $3$d Boundary-Value Problem for a Parabolic Differential-Difference Equation in the One-Dimensional Case
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 636-640.

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

Keywords: parabolic differential-difference equation, elliptic operator, $3$d boundary-value problem, Sobolev space
Mots-clés : interpolation space, Kato's conjecture.
@article{MZM_2012_92_4_a13,
     author = {A. M. Selitskii},
     title = {The {Space} of {Initial} {Data} of the $3$d {Boundary-Value} {Problem} for a {Parabolic} {Differential-Difference} {Equation} in the {One-Dimensional} {Case}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {636--640},
     publisher = {mathdoc},
     volume = {92},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a13/}
}
TY  - JOUR
AU  - A. M. Selitskii
TI  - The Space of Initial Data of the $3$d Boundary-Value Problem for a Parabolic Differential-Difference Equation in the One-Dimensional Case
JO  - Matematičeskie zametki
PY  - 2012
SP  - 636
EP  - 640
VL  - 92
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a13/
LA  - ru
ID  - MZM_2012_92_4_a13
ER  - 
%0 Journal Article
%A A. M. Selitskii
%T The Space of Initial Data of the $3$d Boundary-Value Problem for a Parabolic Differential-Difference Equation in the One-Dimensional Case
%J Matematičeskie zametki
%D 2012
%P 636-640
%V 92
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a13/
%G ru
%F MZM_2012_92_4_a13
A. M. Selitskii. The Space of Initial Data of the $3$d Boundary-Value Problem for a Parabolic Differential-Difference Equation in the One-Dimensional Case. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 636-640. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a13/

[1] A. M. Selitskii, Funct. Differ. Equ., 14:2-4 (2007), 373–395 | MR | Zbl

[2] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., 44, Springer-Verlag, Berlin, 1983 | MR | Zbl

[3] Zh.-L. Lions, E. Madzhenes, Neodnorodnye granichnye zadachi i ikh prilozheniya, T. 1, Mir, M., 1971 | MR | Zbl

[4] R. Seeley, Studia Math., 44 (1972), 47–60 | MR | Zbl

[5] A. Ashyralyev, P. E. Sobolevskii, Well-Posedness of Parabolic Difference Equations, Oper. Theory Adv. Appl., 69, Birkhäuser-Verlag, Basel, 1994 | MR | Zbl

[6] A. L. Skubachevskii, R. V. Shamin, Funct. Differ. Equ., 8:3-4 (2001), 407–424 | MR | Zbl

[7] A. L. Skubachevskii, Elliptic Functional Differential Equations and Applications, Oper. Theory Adv. Appl., 91, Birkhäuser-Verlag, Basel, 1997 | MR | Zbl

[8] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[9] J. L. Lions, J. Math. Soc. Japan, 14:2 (1962), 233–241 | DOI | MR | Zbl

[10] A. McIntosh, Proc. Amer. Math. Soc., 32 (1972), 430–434 | MR | Zbl

[11] P. Auscher, S. Hofmann, A. McIntosch, P. Tchamitchian, J. Evol. Equ., 1:4 (2001), 361–385 | DOI | MR | Zbl

[12] A. Axelsson, S. Keith, A. McIntosh, J. London Math. Soc. (2), 74:1 (2006), 113–130 | DOI | MR | Zbl

[13] R. V. Shamin, Matem. sb., 194:9 (2003), 141–156 | MR | Zbl

[14] E. L. Tsvetkov, Matem. zametki, 51:6 (1992), 107–114 | MR | Zbl