Anisotropic uniqueness classes for a degenerate parabolic equation
Sbornik. Mathematics, Tome 204 (2013) no. 11, pp. 1584-1597 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Anisotropic uniqueness classes of Tacklind type are identified for a degenerate linear parabolic equation of the second order in an unbounded domain. The Cauchy problem and mixed problems with boundary conditions of the first and third type are considered. Bibliography: 18 titles.
Keywords: anisotropic uniqueness class, unbounded domain.
Mots-clés : parabolic equation
@article{SM_2013_204_11_a2,
     author = {V. F. Vil'danova and F. Kh. Mukminov},
     title = {Anisotropic uniqueness classes for a~degenerate parabolic equation},
     journal = {Sbornik. Mathematics},
     pages = {1584--1597},
     year = {2013},
     volume = {204},
     number = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_11_a2/}
}
TY  - JOUR
AU  - V. F. Vil'danova
AU  - F. Kh. Mukminov
TI  - Anisotropic uniqueness classes for a degenerate parabolic equation
JO  - Sbornik. Mathematics
PY  - 2013
SP  - 1584
EP  - 1597
VL  - 204
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/SM_2013_204_11_a2/
LA  - en
ID  - SM_2013_204_11_a2
ER  - 
%0 Journal Article
%A V. F. Vil'danova
%A F. Kh. Mukminov
%T Anisotropic uniqueness classes for a degenerate parabolic equation
%J Sbornik. Mathematics
%D 2013
%P 1584-1597
%V 204
%N 11
%U http://geodesic.mathdoc.fr/item/SM_2013_204_11_a2/
%G en
%F SM_2013_204_11_a2
V. F. Vil'danova; F. Kh. Mukminov. Anisotropic uniqueness classes for a degenerate parabolic equation. Sbornik. Mathematics, Tome 204 (2013) no. 11, pp. 1584-1597. http://geodesic.mathdoc.fr/item/SM_2013_204_11_a2/

[1] A. Tychonoff, “Théorèmes d'unicité pour l'équation de la chaleur”, Matem. sb., 42:2 (1935), 199–216 | Zbl

[2] S. Tacklind, “Sur les class quasianalytiques des solutions des equations aux derivees partielles du type parabolique”, Nova Acta Reg. Soc. Schi. Uppsal. Ser. 4, 10:3 (1936), 3–55

[3] L. M. Kozhevnikowa, “Uniqueness classes for solutions in unbounded domains of the first mixed problem for the equation $u_t=Au$ with quasi-elliptic operator $A$”, Sb. Math., 198:1 (2007), 55–96 | DOI | DOI | MR | Zbl

[4] O. A. Olejnik, E. V. Radkevich, “The method of introducing a parameter in the study of evolutionary equations”, Russian Math. Surveys, 33:5 (1978), 7–84 | DOI | MR | Zbl | Zbl

[5] A. K. Gushchin, “On the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498 | DOI | MR | Zbl

[6] I. M. Sonin, “On uniqueness classes for degenerating parabolic equations”, Math. USSR-Sb., 14:4 (1971), 453–469 | DOI | MR | Zbl | Zbl

[7] L. I. Kamynin, “The uniqueness of the solution of the first boundary value problem in an unbounded domain for a second-order parabolic equation”, U.S.S.R. Comput. Math. Math. Phys., 24:5 (1984), 32–40 | DOI | MR | Zbl

[8] Ya. I. Zhitomirskij, “Uniqueness classes for solutions of the Cauchy problem for linear equations with rapidly increasing coefficients”, Math. USSR-Izv., 1:5 (1967), 1109–1129 | DOI | MR | Zbl | Zbl

[9] O. A. Ladyzhenskaya, “O edinstvennosti resheniya zadachi Koshi dlya lineinogo parabolicheskogo uravneniya”, Matem. sb., 27(69):2 (1950), 175–184 | MR | Zbl

[10] V. F. Gilimshina, F. Kh. Mukminov, “Ob ubyvanii resheniya vyrozhdayuschegosya lineinogo parabolicheskogo uravneniya”, Ufimsk. matem. zhurn., 3:4 (2011), 43–56

[11] O. A. Oleinik, E. V. Radkevich, “Analyticity and theorems of Liouville and Phragmen–Lindelof type for general parabolic systems of differential equations”, Funct. Anal. Appl., 8:4 (1974), 322–330 | DOI | MR | Zbl

[12] O. A. Oleinik, “O edinstvennosti reshenii zadachi Koshi dlya obschikh parabolicheskikh sistem v klassakh bystrorastuschikh funktsii”, UMN, 29:5(179) (1974), 229–230 | MR | Zbl

[13] O. A. Oleinik, G. A. Iosif'yan, “An analogue of Saint-Venant's principle and the uniqueness of solutions of boundary value problems for parabolic equations in unbounded domains”, Russian Math. Surveys, 31:6 (1976), 153–178 | DOI | MR | Zbl | Zbl

[14] L. I. Kamynin, B. N. Khimchenko, “Tikhonov–Petrovskii problem for second-order parabolic equations”, Siberian Math. J., 22:5 (1981), 709–734 | MR | Zbl

[15] F. Kh. Mukminov, “On uniform stabilization of solutions of the first mixed problem for a parabolic equation”, Math. USSR-Sb., 71:2 (1992), 331–353 | DOI | MR | Zbl | Zbl

[16] L. M. Kozhevnikova, “On uniqueness classes of solutions of the first mixed problem for a quasi-linear second-order parabolic system in an unbounded domain”, Izv. Math., 65:3 (2001), 469–484 | DOI | DOI | MR | Zbl | Zbl

[17] V. V. Zhikov, “Weighted Sobolev spaces”, Sb. Math., 189:8 (1998), 1139–1170 | DOI | DOI | MR | Zbl

[18] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'tseva, Linear and quasi-linear equations of parabolic type, Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, RI, 1968 | MR | MR | Zbl | Zbl