An inverse coefficient problem for a parabolic equation with of nonlocal boundary and over determination conditions

Abstract

In this memoir, we have studied an inverse problem for the identification of a coefficient of ther mal diffusivity as a function of time and the distribution of temperature in a one-dimensional diffusion equation with an integral condition when a heat exchange takes place through the material border. We have shown that the inverse problem is well posed under certain regu larity conditions on the data of the problem. The inverse problem is also studied numerically, using the Crankaˆ€“Nicolson finite difference scheme combined with the predictor-corrector technique. We have presented numerical examples to validate the effectiveness of this scheme.