inverse problem

Solving the Cauchy problem for an elliptic equation using Bat Algorithm

This paper presents a method for solving a class of inverse problems for elliptic equations known as the data completion problem.  The goal is to recover missing data on the inaccessible part of the boundary using measurements from the accessible part.  The inherent difficulty of this problem arises from its ill-posed nature, as it is susceptible to variations in the input data.  To address this challenge, the proposed approach integrates Tikhonov regularization to enhance the stability of the problem.  To solve this problem, we use a metaheuristic approach, specificall

Some inverse problem remarks of a continuous-in-time financial model in L^1([t_I,Theta_{max}])

In the paper we are going to introduce an operator that is involved in the inverse problem of the continuous-in-time financial model.  This framework is designed to be used in the finance for any organization and, in particular, for local communities.  It allows to set out annual and multiyear budgets, with describing loan, reimbursement and interest payment schemes.  We discuss this inverse problem in the space of integrable functions over $\mathbb{R}$ having a compact support.  The concept of ill-posedness is examined in this space in order to obtain interesting and u

White dwarfs with rapid rotation

A new analytical approach for calculation of white dwarfs characteristics that accounts for two important competing factors — axial rotation and Coulomb interparticle interactions, is proposed.  The feature of our approach is simultaneous usage of differential and integral forms of equilibrium equation.  In dimensionless form the differential equilibrium equation is strongly nonlinear inhomogeneous equation of the second order in partial derivatives with two dimensionless parameters — the relativistic parameter in stellar center $x_0$ and dimensionless angular velocity

Hemivariational inverse problem for contact problem with locking materials

The aim of this work is to study an inverse problem for a frictional contact model for locking material.  The deformable body consists of electro-elastic-locking materials.  Here, the locking character makes the solution belong to a convex set, the contact is presented in the form of multivalued normal compliance, and frictions are described with a sub-gradient of a locally Lipschitz mapping.  We develop the variational formulation of the model by combining two hemivariational inequalities in a linked system.  The existence and uniqueness of the solution are demonstrated utilizing recent co

Integral conditions in the inverse problems of heat conduction

Thermal processes of new technological methods of heat treatment (thermocyclic, electropulse) of metals and alloys are considered in the paper.  Mathematical models of the temperature field in a moving tape and a wire with cyclically acting pulsed heat sources are considered.  Based on these models, the formulation of inverse problems for homogeneous and inhomogeneous thermal conductivity equations is proposed.  For each case (internal, external heat source or a combination), the appropriate method for solving the inverse problem is proposed.  The integral condition of heat balance is used

Spatial modeling of multicomponent pollution removal for liquid treatment under identification of mass transfer coefficient

A generalized spatial mathematical model of the multicomponent pollutant removal for a liquid treatment is proposed. Under the assumption of domination of convective processes over diffusive ones, the model considers an inverse influence of the determining factor (pollution concentration in water and sludge) on the media characteristics (porosity, diffusion) and takes into account the specified additional condition (overridden condition) for estimation of the unknown mass transfer coefficient of a small value.

Mathematical modeling and interpretaion VES data for a complex surface relief

Algorithms for the mathematical modeling of the direct current electrical prospecting in the 3D complex boundary geomedia are presented. Methods of normalization VES data for the interpretation accounting any surface relief are suggested. Effective algorithms of the direct problem solution for a horizontal layered halfspace are chosen. On the basis of the above the software for electrical prospecting modeling and VES data interpretation is developed.

Solving the inverse problem of seismic prospecting using the energy approach to the analysis of wave fields

In the paper the implementation of energy wave field analysis approach for developed informational model of the geological medium is considered. The solutions of seismic inverse problem are presented, which involves geophysical parameters obtaining of geological medium with the use of field seismic data. In order to obtain geological and geophysical environmental parameters the number of wave field transformations are being carried out, conventionally divided into primary and final part (interpretation).

Identification of mass-transfer coefficient in spatial problem of filtration

A modeling problem of the process of liquid multi component decontamination by a spatial filter is considered, it takes into account the reverse influence of decisive factors (contamination concentrations of liquid and sediment) on characteristics (coefficient of porosity, diffusion) of the medium and gives us the possibility to determine small mass transfer coefficient under the conditions of prevailing of convective constituents over diffusive ones.