Geodesic
A boundary value problem with a conormal derivative for the mixed type equation of second kind with a conjugation condition of the Frankl type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 14-29

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In this paper, using the properties of generalized solutions, both in the hyperbolic part and in the elliptic part of the 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 is investigated. The uniqueness of the solution to the problem under study is proved using the extremum principle, and the existence is proved by the method of integral equations. The theory of singular integral equations, Wiener-Hopf and Fredholm integral equations of the second kind are used to prove the existence of a solution to the problem.
Keywords: equation of the second kind, extremum principle, Wiener-Hopf equation, Green's function, uniqueness and existence of a solution.
Mots-clés : convolution-type equation 
@article{IVM_2022_9_a1,
     author = {B. I. Islomov and A. A. Abdullayev},
     title = {A boundary value problem with a conormal derivative for the mixed type equation of second kind with a conjugation condition of the {Frankl} type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {14--29},
     publisher = {mathdoc},
     number = {9},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_9_a1/}
}
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B. I. Islomov; A. A. Abdullayev. A boundary value problem with a conormal derivative for the mixed type equation of second kind with a conjugation condition of the Frankl type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2022), pp. 14-29. http://geodesic.mathdoc.fr/item/IVM_2022_9_a1/