THE ACCURACY OF THE APPROXIMATE SOLUTIONS TO A BOUNDARY VALUE INVERSE PROBLEM WITH FINAL OVERDETERMINATION

E. V. Tabarintseva

Abstract


The aim of the paper is to investigate the accuracy of the methods  for approximate solving a boundary value inverse problem  with final overdetermination  for a  parabolic equation. We  use the technique of  the continuation to the complex domain and the expansion of the unknown function into  a  Dirichlet series (exponential series) to formulate  the inverse problem as a linear operator equation of the first kind in the appropriate linear normed spaces.  This allows us to estimate the continuity module for the inverse problem   by means of  classical spectral technique   and investigate the order-optimal  approximate methods for the boundary value inverse problem under study.

Keywords


parabolic equation; boundary value inverse problem; module of continuity of the inverse operator; exponential series

Full Text:

PDF

References


Ivanov V.K., Vasin V.V., Tanana V.P. Theory of Linear Ill-Posed Problems and its Applications. Utrecht, VSP, 2002.

Vasil'ev F.P. Optimization Methods. Moscow, Factorial Press, 2002.

Alifanov O.M. Inverse Heat Transfer Problems.

Berlin, Heidelberg, New York, Springer-Verlag, 1994.

Tadi M., Klibanov M.V., Cai Wei An Inversion Method for Parabolic Equations Based on Quasireversibility. Computers and Mathematics with Applications, 2002, vol. 43, no. 8-9, pp. 927-941.

Tabarintseva E.V. On an Estimate for the Modulus of Continuity of a Nonlinear Inverse Problem. Ural Mathematical Journal, 2015, vol. 1, no. 1, pp. 87-92.

Tabarintseva E.V. On Methods to Solve an Inverse Problems for a Nonlinear Differential Equation. Siberian Electronic Mathematical Reports, 2017, vol. 14, no. 17, pp. 199-209.

Tabarintseva E.V. Estimating the Accuracy of a Method of Auxiliary Boundary Conditions in Solving an Inverse Boundary Value Problem for a Nonlinear Equation. textit{Numerical Analysis and Applications, 2018, vol. 11, no. 3, pp. 236-255.

Vasin V.V., Skorik G.G. Solution of the deconvolution problem in the general statement. Trudy Inst. Mat. i Mekh. UrO RAN, 2016, vol. 21, no. 2, pp. 79-99.

Leontev A.F. [ Entire Functions. Series of Exponentials.] Moscow, Nauka, 1983.

Levitan B.M. [Almost-periodic functions]. Moscow, Nauka, 1953.

Denisov A.M. Elements of the Theory of Inverse Problems. Utrecht, VSP, 1999.

Il'in A.M. [The Equations of Mathematical Physics]. Chelyabinsk: Publishing center ChelGU, 2005.

Ivanov V.K., Korolyuk T.I. Error Estimates for Solutions of Incorrectly Posed Linear Problems. USSR Computational Mathematics and Mathematical Physics, 1969, vol. 9, no. 11, pp. 35-49.

Tanana V.P. Methods for Solving Operator Equations. Utrecht, VSP, 2002.


Refbacks

  • There are currently no refbacks.


 Save