On the protective layer boundary determining error in the thermal conductivity inverse problem

Abstract

The article studies the problem of determining the error introduced by the inaccuracy of determining the thickness of a protective heat-resistant coating for composite materials. The mathematical problem is the heat conduction equation on an inhomogeneous half-line. The temperature on the outer side of the half-line (x = 0) is considered unknown on an infinite time interval. To find it, the temperature is measured at the media section at the point x = x0. An analytical study of the direct problem is carried out in the work. It made it possible to formulate the inverse problem mathematically rigorously and to define functional spaces in which it is convenient to solve the inverse problem. The main difficulty to be solved in the article is to obtain an estimate of the approximate solution error. The projection regularization method is used to estimate the modulus of conditional correctness, with the help of which order-exact estimates are obtained.