On a class of problems of determining the temperature and density of heat sources given initial and final temperature

Orazov, I.; Sadybekov, Makhmud A.

doi:10.1134/s0037446612010120

Cited by 78 publications

(36 citation statements)

References 3 publications

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“…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 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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“…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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“…The solvability of various inverse problems for parabolic equations was studied in papers of Anikonov YuE and Belov YuYa, Bubnov BA, Prilepko AI and Kostin AB, Monakhov VN, Kozhanov AI, Kaliev IA, Sabitov KB, and many others. These citations can be seen in Orazov and Sadybekov . In Ahmad et al, there are good references to publications on related issues.…”

Section: Reduction To a Mathematical Problemmentioning

confidence: 99%

“…And the first of conditions (8) means the proportionality of the difference of fluxes across opposite boundaries to the density value at the boundary. We note that in Ahmad et al, 1 the Dirichlet boundary conditions u (− , t) = u ( , t) = 0 were used instead of condition (8).…”

Section: Reduction To a Mathematical Problemmentioning

confidence: 99%

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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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“…Also, differential equations with operations on the space variable received great attention starting with Carleman [6] (equations with shift (involution)) and followed with great attention by Przewoerska-Rolewicz [17,18,19,20,21,22,23], Aftabizadeh et al [1], Andreev [3], [4], Burlutskayaa et al [5], Gupta [7], [8], [9], Watkins [31], Viner [29], [30], and Wiener [32], [33]; for spectral problems and inverse problems for equations with involutions we may cite the recent works of Kaliev et al [10], [11], Sadybekov et al [15], [16], [25], Sarsenbi et al [13], [26] and [27]. The papers of Aliev [2] and Rus [24] concern the maximum principle for equations with a delay in the space variable.…”

Section: Introductionmentioning

confidence: 99%

Inverse problems for a nonlocal wave equation with an involution perturbation

Kirane¹,

Al-Salti²

2016

J. Nonlinear Sci. Appl.

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On a class of problems of determining the temperature and density of heat sources given initial and final temperature

Cited by 78 publications

References 3 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

Inverse problems for a nonlocal wave equation with an involution perturbation

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