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Determining of Coefficients and the Classical Solvability of a Nonlocal Boundary-Value Problem for the Benney–Luke Integro-Differential Equation with Degenerate Kernel

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Abstract

Using the Fourier method of separation of variables, we examine the classical solvability and construct solutions of a nonlocal inverse boundary-value problem for the fourth-order Benney–Luke integro-differential equation with degenerate kernel. We prove the criterion of the unique solvability of the inverse boundary-value problem and examine the stability of solutions with respect to the recovery function.

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Authors and Affiliations

  1. Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, 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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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 156, Mathematical Analysis, 2018.

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Yuldashev, T.K. Determining of Coefficients and the Classical Solvability of a Nonlocal Boundary-Value Problem for the Benney–Luke Integro-Differential Equation with Degenerate Kernel. J Math Sci 254, 793–807 (2021). https://doi.org/10.1007/s10958-021-05341-2

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  • DOI: https://doi.org/10.1007/s10958-021-05341-2

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