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On the Solvability of a Boundary Value Problem for the Laplace Equation on a Screen with a Boundary Condition for a Directional Derivativeстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 27 ноября 2016 г.
- Авторы: Setukha A.V., Yukhman D.A.
- Журнал: Differential Equations
- Том: 52
- Номер: 9
- Год издания: 2016
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1188
- Последняя страница: 1198
- DOI: 10.1134/S001226611609010X
- Аннотация: We consider a three-dimensional boundary value problem for the Laplace equation on a thin plane screen with boundary conditions for the “directional derivative”: boundary conditions for the derivative of the unknown function in the directions of vector fields defined on the screen surface are posed on each side of the screen. We study the case in which the direction of these vector fields is close to the direction of the normal to the screen surface. This problem can be reduced to a system of two boundary integral equations with singular and hypersingular integrals treated in the sense of the Hadamard finite value. The resulting integral equations are characterized by the presence of integral-free terms that contain the surface gradient of one of the unknown functions. We prove the unique solvability of this system of integral equations and the existence of a solution of the considered boundary value problem and its uniqueness under certain assumptions.
- Добавил в систему: Сетуха Алексей Викторович