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A mixed integral equation of mechanics and a generalized projection method of its solution

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Abstract

A mixed multidimensional integral equation containing integral operators of various types is studied. The case in which the equation has one compact, self-adjoint, and strongly positive operator (with constant limits of integration) and two non-self-adjoint integral Volterra operators (with a variable upper limit of integration) is considered. To solve the equation, an effective projection method allowing one to obtain the result in a form with explicitly distinguished principal singularities is proposed.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 117526, Russia

    A. V. Manzhirov

  2. Bauman Moscow State Technical University, Moscow, 107005, Russia

    A. V. Manzhirov

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

    A. V. Manzhirov

Authors
  1. A. V. Manzhirov
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Correspondence to A. V. Manzhirov.

Additional information

Original Russian Text © A.V. Manzhirov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 470, No. 4, pp. 401–405.

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Manzhirov, A.V. A mixed integral equation of mechanics and a generalized projection method of its solution. Dokl. Phys. 61, 489–493 (2016). https://doi.org/10.1134/S1028335816100025

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  • DOI: https://doi.org/10.1134/S1028335816100025

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