Reconstruction of controls in hyperbolic systems by Tikhonov's method with nonsmooth stabilizers / Korotkii A. I.,Gribanova E. I. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2011. - V. 275, l. 1. - P. 68-77.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

The problem of reconstructing unknown controls in hyperbolic systems from the results of approximate observations of motions of these systems is considered. To solve the problem, Tikhonov's method with a stabilizer containing the total time variation of the control is used. The use of such nondifferentiable stabilizer allows us to obtain more precise results in some cases than the approximation of the desired control in Lebesgue spaces. In particular, this method provides the piecewise uniform convergence of regularized approximations and makes possible the numerical reconstruction of the subtle structure of the desired control.

Author keywords:

controlled hyperbolic system; inverse problems of dynamics; Tikhonov's regularization method; classical variation; piecewise uniform convergence ILL-POSED PROBLEMS; BOUNDED VARIATION; REGULARIZATION; APPROXIMATION

DOI:

10.1134/S0081543811090069

Web of Science ID:

ISI:000297915900006

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	DEC
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Keywords-Plus	ILL-POSED PROBLEMS; BOUNDED VARIATION; REGULARIZATION; APPROXIMATION
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	korotkii@imm.uran.ru katuuufka@mail.ru
Funding-Acknowledgement	Ural Branch of the Russian Academy of Sciences within Presidium of the Russian Academy of Sciences {[}09-P-1-1006]; Russian Foundation for Basic Research {[}11-01-00073]
Funding-Text	This work was supported by the Ural Branch of the Russian Academy of Sciences (project no. 09-P-1-1006) within the Program for Fundamental Research of the Presidium of the Russian Academy of Sciences ``Fundamental Problems of Nonlinear Dynamics{''} and by the Russian Foundation for Basic Research (project no. 11-01-00073).
Number-of-Cited-References	35
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	14
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	859ZY