Geodesic
On the first problem for the degenerate parabolic equations with changing time direction
Matematičeskie zametki SVFU, Tome 23 (2016) no. 1, pp. 67-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the properties of solutions of parabolic equations with changing time direction. We prove that the Riesz and Littlewood-Paley conditions for these solutions are equivalent. We demonstrate the unique solvability of the first mixed problem with boundary and initial functions of the space type and also establish the existence of limits in with the weight of the decisions on the sections of the border, which are free from the initial conditions.
Keywords: degenerate equations, changing time direction, functional spaces, integral identities, first mixed problem, solvability. 
@article{SVFU_2016_23_1_a6,
     author = {I. M. Petrushko and M. I. Petrushko},
     title = {On the first problem for the degenerate parabolic equations with changing time direction},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {67--78},
     year = {2016},
     volume = {23},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a6/}
}
TY  - JOUR
AU  - I. M. Petrushko
AU  - M. I. Petrushko
TI  - On the first problem for the degenerate parabolic equations with changing time direction
JO  - Matematičeskie zametki SVFU
PY  - 2016
SP  - 67
EP  - 78
VL  - 23
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a6/
LA  - ru
ID  - SVFU_2016_23_1_a6
ER  - 
%0 Journal Article
%A I. M. Petrushko
%A M. I. Petrushko
%T On the first problem for the degenerate parabolic equations with changing time direction
%J Matematičeskie zametki SVFU
%D 2016
%P 67-78
%V 23
%N 1
%U http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a6/
%G ru
%F SVFU_2016_23_1_a6
I. M. Petrushko; M. I. Petrushko. On the first problem for the degenerate parabolic equations with changing time direction. Matematičeskie zametki SVFU, Tome 23 (2016) no. 1, pp. 67-78. http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a6/

[1] Mikhailov V. P., “On the boundary values of solutions of elliptic equations in domains with a smooth boundary”, Mat. sb., 101:2 (1976), 163–188 | MR

[2] Ladyzhenskaya O. A., Solonnikov V. A., and Uraltseva N. N.,, Linear and quasilinear parabolic equations, Nauka, Moscow, 1967 | MR

[3] Tersenov S. A., The parabolic equations with changing time direction, Inst. Math., Novosibirsk, 1985 | MR

[4] Egorov I. E., Pyatkov S. G., and Popov S. V., Nonclassical operator-differential equations, Nauka, Novosibirsk, 2000 | MR

[5] Pyatkov S .G., “On the solvability of a boundary value problem for a parabolic equation with changing time direction”, Soviet Math. Dokl., 285:6 (1985), 1322–1327 | MR

[6] Pyatkov S. G., Solvability of the initial-boundary value problems for a nonlinear parabolic equation with changing time direction, Novosib. Gos. Univ., Novosibirsk, 1987

[7] Kislov N. V., “Nonhomogeneous boundary value problems for operator- differential equations of mixed type and their applications”, Mat. Sb., 125:1 (1984), 19–37 | MR

[8] Petrushko I. M. and Tchernikh E. V., ““On initial-boundary value problem for equations with changing time direction”, Vestn. MPEI, 2000, no. 6, 60–70

[9] Petrushko I. M., ““On the boundary and initial values of solutions of parabolic equations”, Mat. Sb., 125:4 (1984), 489–521 | MR