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Boundary Value Problem for Third Order Partial Integro-Differential Equation with a Degenerate Kernel

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Abstract

In this paper, we consider the questions of the unique solvability of a boundary value problem for a third-order partial integro-differential equation with a degenerate kernel and multiple characteristics. An explicit solution of the boundary value problem is constructed. In this case, a combination of three methods was used: the method for constructing Green’s function, the method of Fourier series and the Fredholm method for the degenerate kernel.

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Authors and Affiliations

  1. Uzbek–Israel Joint Faculty of High Technology and Engineering Mathematics, National University of Uzbekistan named after M. Ulugbek, 100174, Tashkent, Uzbekistan

    T. K. Yuldashev

  2. Institute of Mathematics named after V. I. Romanovskii at the Academy of Sciences of the Republik of Uzbekistan, 100170, Tashkent, Uzbekistan

    Yu. P. Apakov

  3. Namangan Engineering-Construction Institute, 160103, Namangan, Uzbekistan

    Yu. P. Apakov & A. Kh. Zhuraev

Authors
  1. T. K. Yuldashev
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  2. Yu. P. Apakov
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  3. A. Kh. Zhuraev
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Correspondence to T. K. Yuldashev, Yu. P. Apakov or A. Kh. Zhuraev.

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(Submitted by A. M. Elizarov)

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Yuldashev, T.K., Apakov, Y.P. & Zhuraev, A.K. Boundary Value Problem for Third Order Partial Integro-Differential Equation with a Degenerate Kernel. Lobachevskii J Math 42, 1317–1327 (2021). https://doi.org/10.1134/S1995080221060329

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  • DOI: https://doi.org/10.1134/S1995080221060329

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