Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...

Mathematical model of direct and inverse problems is developed for the flat plate probe which is subjected to timedependent heat flux at one end, while the other end is kept insulated. The direct solution, which is concerned with determination of the temperature distribution in the probe, is developed using an approach based on the method of variation of parameters. The direct solution is used ...

In many industrial applications one wants to determine the temperature on the surface of a body, where the surface itself is inaccessible to measurement [2, 4]. In this case it is necessary to determine surface temperature from a measured temperature history at a fixed location inside the body. This problem is called an inverse heat conduction problem (IHCP). In a one-dimensional setting, assum...

The area of mathematical inverse problems is quite broad and involves the qualitative and quantitative analysis of a wide variety of physical models. Applications include, for example, the problem of inverse heat conduction, image reconstruction, tomography, the inverse scattering problem, and the determination of unknown coefficients or boundary parameters appearing in partial differential equ...

Purpose: of this paper: Aim of this paper is a presentation of the respectively new tool for solving the optimization problems, which is the Harmony Search algorithm in version slightly modified by the authors, used for identifying the thermal conductivity coefficient. Proposed approach is illustrated with an example confirming its usefulness for solving such kinds of problems. Design/methodolo...

In this article, we consider a Cauchy problem of heat equation, that is, determining the unknown temperature and heat flux at an inaccessible boundary from scattered temperature measurements on an accessible boundary or in some interior locations. This method is similar to the boundary control approach proposed by Leevan Ling and Tomoya Takeuchi in [1] where the authors considered a Cauchy prob...

We define and analyze a linear transformation – the heat transform – that allows to map solutions of hyperbolic equations to solutions of corresponding parabolic equations. The inversion of this mapping can be used to transform an inverse problem for the heat equation to a similar problem for the wave equation. This work is motivated by problems of finding interfaces, boundaries and associated ...