ON SOLVABILITY OF SOME NONLOCAL BOUNDARY VALUE PROBLEMS FOR BIHARMONIC EQUATION

被引：12

作者：

Karachik, Valery ^{[1
]}

Turmetov, Batirkhan ^{[2
]}

机构：

[1] Natl Res Univ, South Ural State Univ, Dept Math Anal, Prosp Lenina 76, Chelyabinsk 454080, Russia

[2] Khoja Akhmet Yassawi Int Kazakh Turkish Univ, Dept Math, Sattarkhanov Ave 29, Turkistan 161200, Kazakhstan

来源：

MATHEMATICA SLOVACA | 2020年 / 70卷 / 02期

关键词：

biharmonic equation; nonlocal problem; involution; Neumann type problem; uniqueness; existence; POLYNOMIAL SOLUTIONS; DIRICHLET PROBLEM; POISSON EQUATION; LAPLACE OPERATOR;

D O I：

10.1515/ms-2017-0355

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper a new class of well-posed boundary value problems for the biharmonic equation is studied. The considered problems are nonlocal boundary value problems of Bitsadze-Samarskii type. These problems are solved by reducing them to Dirichlet and Neumann type problems. Theorems on existence and uniqueness of the solution are proved and exact solvability conditions of the considered problems are found. In addition, the integral representations of solutions are obtained. (C) 2020 Mathematical Institute Slovak Academy of Sciences

引用

页码：329 / 342

页数：14

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