On inverse problems for evolutionary systems: Guaranteed estimates and regularized solutions

Kurzhanski, A.B. & Sivergina, I.F. (1991). On inverse problems for evolutionary systems: Guaranteed estimates and regularized solutions. In: Modelling and Inverse Problems of Control for Distributed Parameter Systems. pp. 93-101 Germany: Springer Berlin/Heidelberg. ISBN 978-3-540-46839-4 10.1007/BFb0044486.

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Abstract

This paper deals with the selection of an initial distribution in the first boundary-value problem for the heat equation in a given domain [0,θ]×Ωθ<∞ with zero values on its boundary S so that the deviation of the respective solution from a given distribution would not exceed a preassigned value γ>0. The result is formulated here in terms of the “theory of guaranteed estimation” for noninvertible evolutionary systems. It also allows an interpretation in terms of regularization methods for ill-posed inverse problems and in particular, in terms of the quasiinvertibility techniques of J.-L. Lions and R. Lattes.

Item Type:	Book Section
Additional Information:	Proceedings of IFIP (W.G.7.2)-IIASA Conference, Laxenburg, Austria, July 24–28, 1989
Research Programs:	System and Decision Sciences - Core (SDS)
Depositing User:	Romeo Molina
Date Deposited:	03 May 2016 14:29
Last Modified:	27 Aug 2021 17:41
URI:	https://pure.iiasa.ac.at/13079

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