This article is cited in 4 papers

On the estimate of accuracy of the auxiliary boundary conditions method for solving a boundary value inverse problem for a nonlinear equation

E. V. Tabarintseva

South Ural State University, 76 Lenina av., Chelyabinsk, 454080, Russia

Abstract: An inverse boundary value problem for a nonlinear parabolic equation is considered. Two-way estimates for the norms of values of a nonlinear operator in terms of the norms of values of the corresponding linear operator are obtained. Consequent by the two-way estimates are established for the modulus of continuity of a nonlinear inverse problem in terms of the modulus of continuity of the corresponding linear problem. The auxiliary boundary conditions method to construct stable approximate solutions to the nonlinear inverse problem is used. An accurate in order error estimate for the auxiliary boundary conditions method on a uniform regularization class has been obtained.

Key words: parabolic equation, inverse problem, modulus of continuity of the inverse operator, approximate method, error estimate.

UDC: 517.948

Received: 14.04.2017
Revised: 22.12.2017

DOI: 10.15372/SJNM20180305

 English version: Numerical Analysis and Applications, 2018, 11:3, 236–255

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