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...

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method...

This paper considers a linear one dimensional inverse heat conduction problem with non constant thermal diffusivity and two unknown terms in a heated bar with unit length. By using the WKB method, the heat flux at the end of boundary and initial temperature will be approximated, numerically. By choosing a suitable parameter in WKB method the ill-posedness of solution will be improved. Finally, ...

In this paper, we consider an inverse problem of linear heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation tern from an overspecified condition on the boundary

This work aims at the comparison between a classical regularization technique and a method within the Bayesian framework, as applied to the solution of an inverse heat conduction problem. The two solution approaches compared are Alifanov's iterative regularization technique and the Markov chain Monte Carlo method. The inverse problem examined in this work deals with the estimation of a transien...

We investigate the inverse problem associated with the heat equation involving recovery of initial temperature distribution in a two-layer cylinder with perfect thermal contact at the interface. The heat equation is solved backward in time to obtain a relationship between the final temperature distribution and the initial temperature profile. An integral representation for the problem is found,...

This paper discusses the initial inverse heat problem (backward heat problem) with time-dependent coefficient. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. Two regularization solutions of the backward heat problem will be given by a modified quasi-boundary value method. The Hölder type error estimates between the regularization...

In this paper a variant of nonlinear exponential Euler scheme is proposed for solving heat conduction problems. The method based on iterations where at each iteration linear initial-value problem has to be solved. We compare the backward combined with iterations. For both methods we show monotonicity and boundedness solutions give sufficient conditions convergence Numerical tests are presented ...