Abstract
Conditions, less stringent than those known at present, are found for the stabilization of a solution of a linear differential equation of the form (du/dt) + A(t) u =f(t) in Hilbert space to a solution of the operational equation Ax =f, where A is a positive self-adjoint operator. Some regularization algorithms (in A. N. Tikhonov's sense) for this equation are investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
Ya. I. Al'ber, “Continuous regularization of linear operator equations,” Matem. Zametki,4, No. 5, 503–509 (1968).
M. I. Vishik and L. A. Lyusternik, “Stabilization of solutions of certain differential equations in Hilbert space,” Dokl. Akad. Nauk SSSR,111, No. 1, 12–15 (1956).
S. G. Krein, Linear Differential Equations in Banach Space [in Russian], Moscow (1967).
A. B. Bakushinskii, “Regularization algorithms for linear equations with unbounded operators,” Dokl. Akad. Nauk SSSR,183, No. 1, 12–14 (1968).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 9, No. 4, pp. 415–420, April, 1971.
I wish to thank Ya. I. Al'ber, O. A. Liskovts, and A. M. Il'in for their advice and useful comments.
Rights and permissions
About this article
Cite this article
Bakushinskii, A.B. Stabilization of solutions of linear differential equations in Hilbert space. Mathematical Notes of the Academy of Sciences of the USSR 9, 239–242 (1971). https://doi.org/10.1007/BF01387772
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01387772