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

  • Tynysbek Sh. Kal’menov
  • Berikbol T. TorebekEmail author
Article
  • 39 Downloads

Abstract

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.

Keywords

Elliptic operator Nonlocal boundary conditions Operator with involution Criterion of well-posedness Riesz basis 

Mathematics Subject Classification

Primary 35J25 35C10 Secondary 35P10 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Differential EquationsInstitute of Mathematics and Mathematical ModelingAlmatyKazakhstan
  2. 2.Al-Farabi Kazakh National UniversityAlmatyKazakhstan

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