Electron. J. Diff. Equ., Vol. 2015 (2015), No. 244, pp. 1-9.

Uniqueness of solutions to boundary-value problems for the biharmonic equation in a ball

Valery V. Karachik, Makhmud A. Sadybekov, Berikbol T. Torebek

In this article we study a generalized third boundary-value problem for homogeneous biharmonic equation in a unit ball with general boundary operators up to third order inclusively, containing normal derivatives and Laplacian. A uniqueness theorem for the solution is proved, and some examples are given.

Submitted August 27, 2015. Published September 22, 2015.
Math Subject Classifications: 35J05, 35J25, 26A33.
Key Words: Biharmonic equation; boundary value problem; Laplace operator.

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Valery V. Karachik
Department of Mathematical and Functional Analysis
South Ural State University
454080, 76, Lenin ave., Chelyabinsk, Russia
email: karachik@susu.ru
Makhmud A. Sadybekov
Department of Mathematical Methods in Information Technologies
Institute of Mathematics and Mathematical Modeling
050010 125 Pushkin str., Almaty, Kazakhistan
email: makhmud-s@mail.ru
Berikbol T. Torebek
Department of Differential Equations
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhistan
email: turebekb85@mail.ru

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