Criterion for the basis property of the eigenfunction system of a multiple differentiation operator with an involution

Sadybekov, Makhmud A.; Sarsenbi, A. M.

doi:10.1134/s001226611208006x

Cited by 51 publications

(26 citation statements)

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“…In this paper, we shall use a spectral problem for ordinary differential operators with involution. Such and similar spectral problems are considered in previous studies …”

Section: Reduction To a Mathematical Problemmentioning

confidence: 94%

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

Kirane

Sadybekov

Sarsenbi

2019

Math Methods in App Sciences

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We consider a problem of modeling the thermal diffusion process in a closed metal wire wrapped around a thin sheet of insulation material. The layer of insulation is assumed to be slightly permeable. Therefore, the temperature value from one side affects the diffusion process on the other side. For this reason, the standard heat equation is modified, and a third term with an involution is added. Modeling of this process leads to the consideration of an inverse problem for a one‐dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat equation. Such equations are also called nonlocal subdiffusion equations or nonlocal heat equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right‐hand side of the equation, which depends only on the spatial variable. The conditions for overdefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.

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“…In this paper, we shall use a spectral problem for ordinary differential operators with involution. Such and similar spectral problems are considered in previous studies …”

Section: Reduction To a Mathematical Problemmentioning

confidence: 94%

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

Kirane

Sadybekov

Sarsenbi

2019

Math Methods in App Sciences

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“…Therefore, the detailed study of the spectral properties of spectral problem (3) is natural. The case α = 0 was considered in works [10][11][12]. Similar spectral problem for the first order operator was considered in [9].…”

Section: Theorem 1 Any Eigenfunction Of (3) Is An Eigenfunction Of (1)mentioning

confidence: 99%

Eigenfunctions of a fourth order operator pencil

Sarsenbi¹,

Sadybekov²

2014

AIP Conference Proceedings

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“…(10), (11) belong to the type-(III), then the set of the functions ( ) ∈ 2 (0, 1) such that E&AF system of the perturbed Samarskii-Ionkin problem (9)- (11) does not form even a simple basis in 2 (0, 1) is also dense in 2 (0, 1).…”

Section: Instability Of Basis Propertymentioning

confidence: 99%

“…One aspect of this problem is the fact that an adjoint problem to (9)- (11) is the spectral problem for the loaded differential equation [16]…”

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

See 1 more Smart Citation

On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

Иманбаев

2015

International Journal of Differential Equations

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Criterion for the basis property of the eigenfunction system of a multiple differentiation operator with an involution

Cited by 51 publications

References 1 publication

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

Eigenfunctions of a fourth order operator pencil

On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

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