On the solvability of a nonlocal boundary problem for the Helmholtz operator in a half-disk

Sadybekov, Makhmud A.; Dildabek, Gulnar; Tengayeva, Aizhan

doi:10.18532/caam.97588

Cited by 1 publication

(2 citation statements)

References 10 publications

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“…Functions (12) satisfy the boundary conditions (4) and (5). Substituting (12) into equation (2) and the boundary conditions (3), taking into account (11), for finding unknown functions R k (r) we obtain following problems:…”

Section: Usage Of the Obtained Results For Solving Of The Nonlocal Bomentioning

confidence: 99%

“…And this fact is applied for the solution of a nonlocal initial-boundary problem for the heat equation. It is used in [11] for the solution of a nonlocal boundary value problem for the Helmholtz operator in a half-disc. And also it is used in [12] for the solution of an inverse nonlocal boundary value problem for the heat equation.…”

Section: Statement Of the Problemmentioning

confidence: 99%

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Constructing a basis from systems of eigenfunctions of one not strengthened regular boundary value problem

Sadybekov

Dildabek

Tengayeva

2017

Filomat

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We investigate a nonlocal boundary value spectral problem for an ordinary differential equation in an interval. Such problems arise in solving the nonlocal boundary value problem for partial equations by the Fourier method of variable separation. For example, they arise in solving nonstationary problems of diffusion with boundary conditions of Samarskii-Ionkin type. Or they arise in solving problems with stationary diffusion with opposite flows on a part of the interval. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is comlplete but not forming a basis. Therefore the direct applying of the Fourier method is impossible. Based on these eigenfunctions there is constructed a special system of functions that already forms the basis. However the obtained system is not already the system of the eigenfunctions of the problem. We demonstrate how this new system of functions can be used for solving a nonlocal boundary value problem on the example of the Laplace equation.

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Section: Usage Of the Obtained Results For Solving Of The Nonlocal Bomentioning

confidence: 99%

Section: Statement Of the Problemmentioning

confidence: 99%

Constructing a basis from systems of eigenfunctions of one not strengthened regular boundary value problem

Sadybekov

Dildabek

Tengayeva

2017

Filomat

Self Cite

View full text Add to dashboard Cite

show abstract

On the solvability of a nonlocal boundary problem for the Helmholtz operator in a half-disk

Cited by 1 publication

References 10 publications

Constructing a basis from systems of eigenfunctions of one not strengthened regular boundary value problem

Constructing a basis from systems of eigenfunctions of one not strengthened regular boundary value problem

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