The Riesz bases consisting of eigen and associated functions for a functional differential operator with variable structure

Kurdyumov, V. P.; Хромов, А. П.

doi:10.3103/s1066369x10020052

Cited by 6 publications

(3 citation statements)

References 4 publications

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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%

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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%

“…Such and similar spectral problems are considered in previous studies. [36][37][38][39][40][41][42][43][44][45][46][47] Definition. By a regular solution of the inverse problem (5) to (8), we mean a pair of functions (u(x, t), (x)) of the class u(x, t) ∈ C 2,1…”

Section: Reduction To a Mathematical Problemmentioning

confidence: 99%

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

Kirane

Sadybekov

Sarsenbi

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…In this paper we shall use a spectral problem for an ordinary differential operators with involution. Such and similar spectral problems were considered in [29][30][31][32][33][34][35][36][37][38][39][40]. When one uses the method of separation of variables to solve the problem, a spectral problem appears, which is mentioned in the next section.…”

Section: Reduction To a Mathematical Problemmentioning

confidence: 99%

On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data

Sadybekov

Dildabek

Ivanova

2018

Advances in Mathematical Physics

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We consider an inverse problem for a one-dimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. The inverse problem consists in the restoration (simultaneously with the solution) of an unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for redefinition 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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Description of spectral properties of a generalized spectral problem with involution for differentiation operator of the second order

Sadybekov¹,

Sarsenbi²,

Tengayeva³

2016

AIP Conference Proceedings

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The Riesz bases consisting of eigen and associated functions for a functional differential operator with variable structure

Cited by 6 publications

References 4 publications

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

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

On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data

Description of spectral properties of a generalized spectral problem with involution for differentiation operator of the second order

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