A method for solving ill-posed nonlocal problem for the elliptic equation with data on the whole boundary

被引：0

作者：

Kal'menov, Tynysbek Sh. ^{[1
]}

Torebek, Berikbol T. ^{[1
,2
]}

机构：

[1] Inst Math & Math Modeling, Dept Differential Equat, Pushkin St 125, Alma Ata 050010, Kazakhstan

[2] Al Farabi Kazakh Natl Univ, Al Farabi Ave, Alma Ata 050040, Kazakhstan

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2019年 / 10卷 / 01期

关键词：

Elliptic operator; Nonlocal boundary conditions; Operator with involution; Criterion of well-posedness; Riesz basis; Primary; 35J25; 35C10; Secondary; 35P10; MIXED CAUCHY-PROBLEM; STRONG SOLVABILITY; LAPLACE; REGULARIZATION; CRITERION;

D O I：

10.1007/s11868-017-0231-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper a nonlocal problem for the elliptic equation in a cylindrical domain is considered. It is shown that this problem is ill-posed as well as the Cauchy problem for the Laplace equation. The method of spectral expansion in eigenfunctions of the nonlocal problem for equations with involution establishes a criterion of the strong solvability of the considered nonlocal problem. It is shown that the ill-posedness of the nonlocal problem is equivalent to the existence of an isolated point of the continuous spectrum for a nonself-adjoint operator with involution.

引用

页码：177 / 185

页数：9

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