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Determination of the coefficient and boundary regime in boundary value problem for integro-differential equation with degenerate kernel

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Abstract

This article examines questions of unique solvability for an inverse boundary value problem to recover the coefficient and boundary regime of a nonlinear integro-differential equation with degenerate kernel. We propose a novel method of degenerate kernel for the case of inverse boundary value problem for the considered ordinary integro-differential equation of second order. By the aid of denotation, the integro-differential equation is reduced to a system of algebraic equations. Solving this system and using additional conditions, we obtained a system of two nonlinear equations with respect to the first two unknown quantities and a formula for determining the third unknown quantity. We proved the single-value solvability of this system using the method of successive approximations.

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Authors and Affiliations

  1. Department of Higher Mathematics, Siberian State Aerospace University, Institute of Informatics and Telecommunication, pr. Krasnoyarskii Rabochii 31, Krasnoyarsk, 660014, Russia

    T. K. Yuldashev

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  1. T. K. Yuldashev
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Correspondence to T. K. Yuldashev.

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Submitted by E. K. Lipachev

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Yuldashev, T.K. Determination of the coefficient and boundary regime in boundary value problem for integro-differential equation with degenerate kernel. Lobachevskii J Math 38, 547–553 (2017). https://doi.org/10.1134/S199508021703026X

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