In this article, we consider an inverse heat conduction problem in one-dimensional space with two unknown terms. In this problem, the initial temperature and histories of temperature in the finite interval of time, may be determined. Then, by using a semi-implicit finite difference method, an estimation of these unknown terms will be found. Obviously, this problem is ill-posed. But by applying ...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

This note considers the problem of estimating unknown time-varying strength of the temporal-dependent heat source, from measurements of the temperature inside the square domain, when the prior knowledge of the source functions is not available. This problem is an inverse heat conduction problem. In this process, the direct problem will be solved by using the heat fundamental solution. Then a se...

In this paper we investigate the stability and convergence rates of the widely used output least-squares method with Tikhonov regularization for the identification of the conductivity distribution in a heat conduction system. Due to the rather restrictive source conditions and regularity assumptions on the nonlinear parameter-to-solution operator concerned, the existing Tikhonov regularization ...

‎In this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎Using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎For the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎It is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...