Abstract
The dependence of the uniqueness classes of the solutions of boundary value problems for second-order parabolic equations on the coefficients of the equation and on the geometry of an unbounded domain is investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. N. Tikhonov, “Uniqueness theorems for the heat equation,” Mat. Sb.,42, No. 2, 64–95 (1935).
S. Täcklind, “Sur les classes quasianalitiques des solutions des équations aux derivées partielles du type parabolique,” Nova Acta Regial Soc. Scientiarum Uppsaliensis, Ser. 4,10, No. 3, 3–55 (1936).
I. G. Petrovskii, “On certain problems of the theory of partial differential equations,” Uspekhi Mat. Nauk,1, Nos. 3–4, 44–70 (1946).
A. M. Il'in, A. S. Kalashnikov, and O. A. Oleinik, “Second-order linear equations of parabolic type,” Uspekhi Mat. Nauk,17, No. 3, 3–146 (1962).
O. A. Oleinik and E. V. Radkevich, “The method of introducing a parameter for the investigation of evolution equations,” Uspekhi Mat. Nauk,33, No. 5, 7–76 (1978).
A. G. Gagnidze, “Investigation of second-order parabolic equations with growing coefficients by the method of introducing a parameter,” Vestnik Moskov. Univ., Ser. I Mat. Mekh., No. 5, 33–37 (1981).
O. A. Oleinik and 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,” Uspekhi Mat. Nauk,31, No. 6, 142–166 (1976).
O. A. Oleinik, “On examples of nonuniqueness of the solution of a boundary value problem for a parabolic equation in an unbounded domain,” Uspekhi Mat. Nauk,38, No. 1 (229), 183–184 (1983).
E. M. Landis, “The dependence of the uniqueness classes of the solutions of the second initial-boundary value problem for the heat equation in an unbounded domain on the geometry of the domain,” Dokl. Akad. Nauk SSSR,275, No. 4, 790–793 (1984).
A. G. Gagnidze, “On the uniqueness classes of the solutions of boundary vlaue problems for second-order parabolic equations in an unbounded domain,” Uspekhi Mat. Nauk,39, No. 6, 193–194 (1984).
Additional information
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 123–136, 1988.
Rights and permissions
About this article
Cite this article
Gagnidze, A.G. Uniqueness of solutions of boundary value problems in unbounded domains for parabolic equations. J Math Sci 50, 1437–1446 (1990). https://doi.org/10.1007/BF01388507
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01388507