Mathematical modeling of non-equilibrium sorption

Kaliev, I. A.; Mukhambetzhanov, S. T.; Sabitova, G. S.; Sakhit, Anghyz E.

doi:10.1063/1.4959668

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…In work [4], a global unique solvability was proved for the Dirichlet initial-boundary problem for system (1)-(2). In [5], [6] there was formulated a difference approximation of the differential problem by an implicit scheme, a solution to the difference problem was constructed by means of the sweep method and the results of the numerical experiments were presented.…”

Section: Formulation Of Problemmentioning

confidence: 99%

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Neumann boundary value problem for system of equations of non-equilibrium sorption

Kaliev

Sabitova

2019

Ufimsk. Mat. Zh.

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Filtration of liquids and gases containing associated (dissolved, suspended) solids in porous media is accompanied by diffusion of these substances and mass transfer between the liquid (gas) and solid phases. In this work, we study the system of equations modeling the process of a non-equilibrium sorption. We prove an existence and uniqueness theorem for a multi-dimensional Neumann initial-boundary value problem in the Hölder classes of functions. We obtain a maximum principle, which plays an important role in the proof of the theorem. The uniqueness of the solution follows this principle. The existence of a solution to the problem is shown by Schauder fixed point theorem for a completely continuous operator; we describe a corresponding operator. We obtain estimates ensuring the complete continuity of the constructed operator and the mapping of some closed set of functions into itself over a small time interval. Then we obtain the estimates allowing us to continue the solution up to arbitrary finite time.

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Section: Formulation Of Problemmentioning

confidence: 99%

“…Estimate 7is implied by representation (8) with employing (6). Indeed, since 0 ( ) 0, ( , ) 0, it follows from (8) that ( , ) 0 for all ( , ) ∈ .…”

Section: Proof Of Theoremmentioning

confidence: 99%

Neumann boundary value problem for system of equations of non-equilibrium sorption

Kaliev

Sabitova

2019

Ufimsk. Mat. Zh.

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“…The solvability of various inverse problems for parabolic equations was studied in many papers [1][2][3][4][5][6][7]. Paper [8] is most close to the subject of this one.…”

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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“…In [6] the global unique solvability of the first initial-boundary value problem for system (1)-(2) is proved. In [7,8], a difference approximation of the differential problem was formulated using an implicit scheme, a solution of the difference problem was constructed using the sweep method, and the results of numerical experiments were presented.…”

Section: Introductionmentioning

confidence: 99%

The third boundary value problem for the system of equations of non-equilibrium sorption

Kaliev¹,

Sabitova²

2018

Sib. Elektron. Mat. Izv.

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All Russian mathematical portal I. A. Kaliev, G. S. Sabitova, The third boundary value problem for the system of equations of non-equilibrium sorption, Sib.Abstract. In this paper, we investigate the system of equations modeling the process of non-equilibrium sorption. In particular, such systems are used in mathematical modeling of the production process of the useful component by the method of borehole underground leaching. The theorem of existence and uniqueness of the solution of the third boundary value problem in the multidimensional case in Hölder classes of functions is proved. The obtained maximum principle plays an important role in the proof of the theorem. The uniqueness of the solution is a consequence of this principle. The existence of a solution to the problem is shown by Schauder's fixed point theorem of a completely continuous operator. The description of the corresponding operator is given. Estimates are obtained to ensure the continuity of the constructed operator, and it is shown that the operator maps the original set of functions into itself at a small period of time. Then the estimates are given, allowing to continue the solution to any finite value of time.Keywords: process of non-equilibrium sorption, third boundary value problem, global single-valued solvability.Kaliev, I.A., Sabitova, G.S., The third boundary value problem for the system of equations of non-equilibrium sorption.c ⃝ 2018 Kaliev I.A., Sabitova G.S.

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Mathematical modeling of non-equilibrium sorption

Cited by 3 publications

References 2 publications

Neumann boundary value problem for system of equations of non-equilibrium sorption

Neumann boundary value problem for system of equations of non-equilibrium sorption

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

The third boundary value problem for the system of equations of non-equilibrium sorption

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