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Iterative Method for the Numerical Solution of an Inverse Coefficient Problem for a System of Partial Differential Equations

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Abstract

For a system of partial differential equations, we consider the inverse problem of determining one of the coefficients based on additional information on one of the solution components. An iterative method is proposed for calculating the unknown coefficient based on the reduction of the inverse problem to a nonlinear operator equation. The convergence of the iterative method and the existence and uniqueness of a solution of the inverse problem are proved. Numerical results illustrating the convergence of the iterative numerical method are given.

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Funding

This work was supported by the Moscow Center for Fundamental and Applied Mathematics.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    A. M. Denisov & A. A. Efimov

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  1. A. M. Denisov
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  2. A. A. Efimov
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Correspondence to A. M. Denisov or A. A. Efimov.

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Translated by V. Potapchouck

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Denisov, A.M., Efimov, A.A. Iterative Method for the Numerical Solution of an Inverse Coefficient Problem for a System of Partial Differential Equations. Diff Equat 56, 900–909 (2020). https://doi.org/10.1134/S0012266120070095

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  • DOI: https://doi.org/10.1134/S0012266120070095

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