On an inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

Orazov, I.; Sadybekov, Makhmud A.

doi:10.1063/1.4930431

Cited by 7 publications

(5 citation statements)

References 18 publications

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“…Hence in view of the absolute convergence of series (13) and estimates (14), we conclude that series (7) converge and the solution to problem (1)-(3) belongs to classes u(x,t) ∈ W 2,1 2 (Ω), f (x) ∈ L 2 (0, 1).…”

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confidence: 66%

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An inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

Orazov¹,

Makhatova²

2014

AIP Conference Proceedings

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In this paper, we consider one family of problems simulating the determination of target components and density of sources from given values of the initial and final states. The mathematical statement of these problems leads to the inverse problem for the diffusion equation, where it is required to find not only a solution of the problem, but also its right-hand side that depends only on a spatial variable. A specific feature of the considered problems is that the system of eigenfunctions of the multiple differentiation operator subject to boundary conditions of the initial problem does not have the basis property. We prove the unique existence of a generalized solution of the problem.

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confidence: 66%

“…Let us cite papers only those of them that are most close to the subject under consideration [12][13][14][15][16].…”

Section: The Mathematical Problemmentioning

confidence: 99%

An inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

Orazov¹,

Makhatova²

2014

AIP Conference Proceedings

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“…In Ahmad et al, there are good references to publications on related issues. We note from recent papers close to the theme of our article. In these papers, different variants of direct and inverse initial‐boundary value problems for evolutionary equations are considered, including problems with nonlocal boundary conditions and problems for equations with fractional derivatives.…”

Section: Reduction To a Mathematical Problemmentioning

confidence: 85%

“…Thus, (23) holds if and only if k,i = 0 for all values of the indexes k, i. This is possible only in the case…”

Section: Construction Of a Formal Solution Of The Problemmentioning

confidence: 99%

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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“…is a partial solution of the inhomogeneous equation (21). Therefore, we obtain a unique solution of the Cauchy problem (21)- (22) in the following form:…”

Section: Uniqueness Of the Solution Of The 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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On an inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

Cited by 7 publications

References 18 publications

An inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

An inverse problem of mathematical modeling of the extraction process of polydisperse porous materials

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

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