Abstract
We study the problem for Shilov parabolic equations of arbitrary order with constant coefficients with conditions nonlocal in time and periodic in space variables. We establish conditions for the existence and uniqueness of a classical solution of the problem and prove metric theorems on lower bounds of small denominators appearing in the construction of a solution of the problem.
Similar content being viewed by others
References
V. I. Bernik, B. I. Ptashnik, and B. O. Salyga, “An analog of the many-point problem for a hyperbolic equation with constant coefficients,”Differents. Uravn.,13, No. 4, 637–645 (1977).
A. A. Dezin, “Operators with the first derivative with respect to “time” and nonlocal boundary conditions,”Izv. Akad. Nauk SSSR, Ser. Mat.,31, No. 1, 144–149 (1967).
V. S. Il'kiv, “A nonlocal boundary-value problem for partial differential equations of infinite order,”Ukr. Mat. Zh.,35, No. 4, 498–502 (1983).
V. S. Il'kiv and B. I. Ptashnik, “A problem with nonlocal boundary conditions for systems of partial differential equations with constant coefficients,”Differents. Uravn.,20, No. 16, 1012–1023 (1984).
I. Ya. Kmit',Nonlocal Problems for Second-Order Hyperbolic Equations [in Russian], Dep. UkrNIINTI, No. 842-Uk.91, L'vov (1991).
A. M. Nakhushev, “Nonlocal boundary-value problems with shift and their relation to weighted equations,”Differents. Uravn.,21, No. 1, 92–101 (1985).
B. I. Ptashnik,Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
V. G. Romanov, “On local solvability of many-dimensional inverse problems for hyperbolic equations,”Differents. Uravn.,25, No. 2, 275–283 (1989).
V. I. Gorbachuk and M. L. Gorbachuk,Boundary-Value Problems for Operator-Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1621–1626, December, 1994.
The work was supported by the Foundation for Fundamental Studies of Ukrainian State Committee on Science and Technology.
Rights and permissions
About this article
Cite this article
Zadorozhna, N.M., Mel'nik, O.M. & Ptashnik, B.I. Nonlocal boundary-value problem for parabolic equations. Ukr Math J 46, 1795–1802 (1994). https://doi.org/10.1007/BF01063168
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01063168