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A Boundary Value Problem with a Conormal Derivative for a Mixed-Type Equation of the Second Kind with a Conjugation Condition of the Frankl Type

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Abstract

In this paper, using the properties of generalized solutions in both the hyperbolic part and the elliptic part of a mixed domain, we study a boundary value problem with a conormal derivative for a mixed type equation of the second kind with Frankl-type conditions. The uniqueness of the solution to the problem under study is proven using the extremum principle, and its existence is proven by the method of integral equations. The theory of singular integral equations and Wiener–Hopf and Fredholm integral equations of the second kind are used to prove the existence of a solution to the problem.

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Authors and Affiliations

  1. Ulugbek National University of Uzbekistan, 700174, Tashkent, Republic of Uzbekistan

    B. I. Islomov

  2. Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 100000, Tashkent, Republic of Uzbekistan

    A. A. Abdullayev

Authors
  1. B. I. Islomov
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  2. A. A. Abdullayev
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Correspondence to B. I. Islomov or A. A. Abdullayev.

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Islomov, B.I., Abdullayev, A.A. A Boundary Value Problem with a Conormal Derivative for a Mixed-Type Equation of the Second Kind with a Conjugation Condition of the Frankl Type. Russ Math. 66, 11–25 (2022). https://doi.org/10.3103/S1066369X2209002X

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