Solution of some inverse problems in nonequilibrium sorption dynamics

“…Usually these problems consist in determining a coefficient of an equation, the sought coefficient depending on the solution, basing on the additional information about the solution. A large number of papers are devoted to inverse problems of such a type; see, e.g., [1,4,5,7). Of much importance for analysis of such problems and development of numerical methods for their solution is the study of the uniqueness of their solution in classes of functions of finite smoothness.…”

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confidence: 99%

An inverse problem for a nonlinear mathematical model of sorption dynamics with mixed-diffusional kinetics

Денисов¹,

Lamos²

1996

Journal of Inverse and Ill-Posed Problems

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Inverse problems for coefficients of nonlinear differential equations arise in investigation of various processes in heat physics, physical chemistry, hydrogeology, nuclear physics, and other sciences. Usually these problems consist in determining a coefficient of an equation, the sought coefficient depending on the solution, basing on the additional information about the solution. A large number of papers are devoted to inverse problems of such a type; see, e.g., [1,4,5,7). Of much importance for analysis of such problems and development of numerical methods for their solution is the study of the uniqueness of their solution in classes of functions of finite smoothness. Theorems of uniqueness in such classes of functions were usually proved under the assumption that the sought coefficient is known for small values of the argument [2,6,9]. A method was first proposed in [3] making it possible to prove the uniqueness of the solution to an inverse problem on the whole and without the above-mentioned assumption. This method is applied in the present paper for study of the inverse problem for a nonlinear mathematical model of sorption dynamics with mixed-diffusional kinetics.

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“…This inverse problem involves determining the solution-dependent coefficient of a system of partial differential equations with additional information about the solution given in the form of a time function. Uniqueness of the solution of the inverse problem is proved.Inverse problems of sorption dynamics have been discussed often in the literature (see, e.g., [1][2][3][4][5][6][7]). A method for investigating inverse coefficient problems for mathematical models of sorption dynamics in the class of functions of finite smoothness has been proposed in [6].…”

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The problem of determining the kinetic coefficient in a mathematical model of sorption dynamics

Денисов¹,

Lamos²

1999

Comput Math Model

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The problem of determining the concentration-dependent kinetic coefficient is considered for the nonlinear mathematical model of sorption dynamics with mixed diffusion kinetics. This inverse problem involves determining the solution-dependent coefficient of a system of partial differential equations with additional information about the solution given in the form of a time function. Uniqueness of the solution of the inverse problem is proved.Inverse problems of sorption dynamics have been discussed often in the literature (see, e.g., [1][2][3][4][5][6][7]). A method for investigating inverse coefficient problems for mathematical models of sorption dynamics in the class of functions of finite smoothness has been proposed in [6]. In [7] this method has been applied to the problem of determining the sorption isotherm for a mathematical model of sorption dynamics with mixed diffusion kinetics. In the present article we apply the same model to examine the problem of determining the solution-dependent kinetic coefficient.Consider the mathematical model of sorption dynamics with mixed diffusion kinetics for the case of concentration-dependent kinetic coefficient:Here Or = {(x,t) :O <_ x <_ l,O <_ t <_ r}and cr, y, X are positive constants, ), > 1. The functions 13(s), F(s), and Ix(t) satisfy the following conditions:

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Solution of some inverse problems in nonequilibrium sorption dynamics

Cited by 4 publications

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Determination of a nonlinear coefficient in a hyperbolic equation for the Goursat problem

Determination of a nonlinear coefficient in a hyperbolic equation for the Goursat problem

An inverse problem for a nonlinear mathematical model of sorption dynamics with mixed-diffusional kinetics

The problem of determining the kinetic coefficient in a mathematical model of sorption dynamics

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