Mathematical modeling numerical determination of coefficients in some mathematical models of nonisothermal sorption dynamics

We consider inverse problems for mathematical models of sorption dynamics that allow for diffusion, heat balance, and two types of kinetics assuming temperature-dependent kinetic coefficients. Two methods for numerical solution of inverse problems are proposed. Their efficiency is investigated by computer experiments.     

Inverse problems for a mathematical model of redox sorption

We consider a mathematical model of sorption that allows for external diffusion kinetics and a redox reaction. Two inverse problems are considered for this model, uniqueness is proved, and numerical solution methods are proposed. The efficiency of the numerical methods is investigated by computer experiments. __________ Translated from Prikladnaya Matematika i Informatika, No. 23, pp. 15–23, 2006.     

Numerical determination of the sorption isotherm for nonisothermal sorption

Two mathematical models of sorption dynamics are considered, one allowing for external diffusion kinetics and the other for internal diffusion kinetics with heat balance. Two inverse problems are investigated for these models and numerical solutions are proposed. The efficiency of the numerical methods is studied in a computer experiment. __________ Translated from Prikladnaya Matematika i Informatika, No. 28, pp. 37–43, 2008.     

Iterative methods for solving inverse problems for nonlinear partial differential equations

Inverse coefficient problems are considered for the mathematical models of sorption dynamics and heat conduction. Iterative methods proposed for solving these inverse problems transform a supplementary condition into an integral relationship containing the unknown coefficient. Combined with the original boundary-value problem, this integral relationship makes it possible to construct an iterative process. A priori representation of the unknown nonlinear coefficients in parametric form is not required. Results of computational experiments are reported.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 142–149.     

Numerical Solution of the Inverse Nonequilibrium Sorption Problem with a Time-Dependent Boundary Condition

We consider the quasi-linear problem of nonequilibrium sorption dynamics with external-diffusion kinetics and a boundary condition that contains the time derivative of a solution component. A numerical method is proposed for describing the inverse problem to recover the nonlinear parameter of the system of differential equations—the inverse of the sorption isotherm. Convergence of the difference scheme for the direct problem is proved. Numerical solutions of both the direct and the inverse problem are obtained for various parameter values.     

Numerical solution of an inverse problem for a two-dimensional mathematical model of sorption dynamics

We consider a two-dimensional mathematical model of sorption that allows for inner-diffusion kinetics as well as longitudinal and transverse diffusion. The inverse problem of determining the sorption isotherm from an experimental dynamic output curve is investigated for this model and stable solution methods are proposed for the inverse and the direct problem. The efficiency of the solution methods is explored in computer experiments.     

Numerical solution of an inverse problem of nonisothermal sorption dynamics

We consider the inverse problem for a mathematical model of sorption dynamics that incorporates diffusion, intradiffusion kinetics, and the heat balance. Two numerical methods are proposed. Their efficiency is investigated in a computer experiment. Translated from Prikladnaya Matematika i Informatika, No. 29, pp. 56–63, 2008.     

Unique Solvability of the Inverse Problem with a Time-Dependent Boundary Condition for a Sorption Model

A mixed initial boundary-value problem is considered for nonequilibrium sorption dynamics with inner-diffusion kinetics. The problem allows for convection and longitudinal diffusion and has a time-dependent boundary condition. This condition contains the time derivative of a solution component and constitutes the balance equation for the absorbed mixture near the output boundary of the sorption region—inside the diffusion barrier. Bounds on the solution of the direct problem are obtained: nonnegativity of the solution and its first time derivatives, and boundedness of the solution by known functions. The inverse problem of estimating the nonlinear system parameter—the sorption isotherm—is considered and a uniqueness theorem is proved.     

The theory of inverse boundary problems for analytic functions and its applications

Questions of the well-posedness of inverse boundary problems on the plane and on Riemann surfaces, results on the univalent solvability of inverse boundary problems and on the corresponding parts of the geometric theory of functions of a complex variable, various inverse problems of hydroaeromechanics, and also inverse problems of pressured and unpressured filtration, mathematical and applied aspects of inverse problems on change of contours are presented.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 18, pp. 67–124, 1980.     

Numerical inversion of heat exchange coefficient and source sink term for a thermal-fluid coupled model in porous medium

Abstract

In this paper, we focus on three inverse problems for a coupled model from temperature-seepage field in high-dimensional spaces. These inverse problems aim to determine an unknown heat transfer coefficient and a source sink term in seepage continuity equation with specified initial-boundary conditions and additional measurements. Some finite difference schemes of coupled equations are presented and analyzed.Three algorithms for these inverse problems are proposed. Some numerical experiments are provided to assert the accuracy and efficiency of proposed algorithms.     

Quasi-one-dimensional method for the two-dimensional magnetotelluric sounding inverse problem

The two-dimensional magnetotelluric sounding inverse problem is solved by a quasi-one-dimensional method. A linearization method is proposed for one-dimensional inverse problems. The appearance of false conducting structures in the solution of the inverse problem is considered and some counter-measures are suggested. The quasi-one-dimensional method is applicable to many-dimensional magnetotelluric sounding inverse problems if the electrical conductivity is a priori known to vary slowly along the Earth’s surface. __________ Translated from Prikladnaya Matematika i Informatika, No. 22, pp. 5–11, 2005.     

On inverse limits of monounary algebras

We study inverse limits of monounary algebras. All monounary algebras A such that A can arise from A only by an inverse limit construction are described. We deal with an existence of an inverse limit. Some inverse limit closed classes are described. The paper ends with two problems.     

To solving inverse eigenvalue problems for parametric matrices

Some statements of inverse eigenvalue problems for one-parameter and multiparameter regular polynomial matrices with linear and nonlinear dependences on spectral parameters are considered. Methods for solving inverse eigenvalue problems based on rank factorization, exhaustion, and reduction to nonlinear equations are proposed. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 174–192.     

Application of Tikhonov’s regularization method to solve inverse problems for two population models

Tikhonov’s regularization method is applied to numerical solution of inverse problems for two population models. For the first model we solve the inverse problem that involves simultaneous determination of the mortality rate and the initial distribution of individuals given supplementary information on population density. For the second model we determine the growth rate of the individuals given additional information about their density. Examples of numerical solution are presented for both inverse problems. __________ Translated from Prikladnaya Matematika i Informatika, No. 23, pp. 5–14, 2006.     

Boundary control and inverse problems: The one-dimensional variant of the BC-method

This is the first paper of a conceived series under the common title “The boundary control method in inverse problems.” The aim of the series is to expound systematically an approach to inverse problems based upon its relationship with control theory. The 1d-variant of the method is shown with the example of the classical problem of recovering the density of an inhomogeneous string, and both dynamical and spectral statements of the problem are considered. The paper is written in such a way as to serve as an introduction to the multidimensional BC-method: the basic tools and constructions are amenable to further generalization to multidimensional problems. Bibliography: 31 titles. To the 70th birthday of A. S. Blagoveshchenskii, my teacher and one of the pioneers in dynamical inverse problems __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 19–80.     

Reconstruction of the medium by iterative-asymptotic method

Interpretation of geoelectric fields gives rise to multidimensional inverse problems, which include many problems for quasi-layered media. Such problems are solved by an iterative-asymptotic method. In the present article we consider a particular implementation of the method designed for a certain model of the medium, a certain method of solving the one-dimensional inverse problem, and a certain representation of magnetotelluric sounding data. Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 44–55, 1999.     

Stability of inverse problems in an infinite slab with partial data

In this paper, we study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrödinger equation and by Krupchyk, Lassas, and Uhlmann for the case of the magnetic Schrödinger equation. Here, we quantify the method of uniqueness proposed by Li and Uhlmann and prove a log–log stability estimate for the inverse problems associated to the Schrödinger equation. The boundary measurements considered in these problems are modeled by partial knowledge of the Dirichlet-to-Neumann map: in the first inverse problem, the corresponding Dirichlet and Neumann data are known on different boundary hyperplanes of the slab; in the second inverse problem, they are known on the same boundary hyperplane of the slab.     

A global in time existence and uniqueness result for an integrodifferential hyperbolic inverse problem with memory effect

We consider an inverse problem for a one-dimensional integrodifferential hyperbolic system, which comes from a simplified model of thermoelasticity. This inverse problem aims to identify the displacement u, the temperature η and the memory kernel k simultaneously from the weighted measurement data of temperature. By using the fixed point theorem in suitable Sobolev spaces, the global in time existence and uniqueness results of this inverse problem are obtained. Moreover, we prove that the solution to this inverse problem depends continuously on the noisy data in suitable Sobolev spaces. For this nonlinear inverse problem, our theoretical results guarantee the solvability for the proposed physical model and the well-posedness for small measurement time τ, which is quite different from general inverse problems.     

On the unsolvability of inverse singular value problems almost everywhere

In this paper, the unsolvability of inverse singular value problems almost everywhere is discussed. Applying the method described by Sun and Ye [J Comput Math. 1986;4:212–226], a sufficient condition is given such that the inverse singular value problems are unsolvable almost everywhere. This result shows that inverse singular value problems are unsolvable almost everywhere if the multiplicity of zero singular values is sufficiently large.     

哈明距离下的网络逆问题研究综述

逆优化问题研究的是如何改变原问题中的权参数,使得某些给定的解是问题在新的权参数下的最优解,且使总的改造费用尽可能少.作为逆优化问题中相对较新的一个分支,哈明距离下的网络逆问题具有较大的理论研究及实际应用价值.此文首先介绍了逆优化问题和哈明距离下的网络逆问题以及它们的应用,然后详细介绍了哈明距离下的网络逆问题的研究动态及使用的研究方法.最后给出了该领域中的一些值得研究的问题.