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The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane

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Abstract

We prove existence and uniqueness theorems for the solution of the inverse problem of simultaneous determination of the t-dependent coefficients of u and ux in a nondivergent parabolic equation with two independent variables from integral observation of x. Estimates of the maxima of the moduli of these coefficients with constants explicitly expressed in terms of the input data of the problem are given. An example of an inverse problem to which the proved theorems apply is presented.

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Funding

This work was supported by the Program for the Enhancement of the Competitiveness of NRNU MEPhi (grant no. 02.a03.21.0005 of August 27, 2013).

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  1. National Research Nuclear University MEPhI, Moscow, 115409, Russia

    V. L. Kamynin

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  1. V. L. Kamynin
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Correspondence to V. L. Kamynin.

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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 1, pp. 74–86.

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Kamynin, V.L. The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane. Math Notes 107, 93–104 (2020). https://doi.org/10.1134/S0001434620010095

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  • DOI: https://doi.org/10.1134/S0001434620010095

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