On Approximate Solution of Inverse Problem for Nonlinear Equation with Discontinuous Coefficient

We study a backward boundary value problem for a nonlinear heat transfer equation with a discontinuous coefficient. The mathematical model under study describes intensive heat conductivity or diffusion processes in a medium consisting of different materials. The model is used to study composite materials. We use the auxiliary boundary conditions method to get stable numerical solutions of the inverse problem. We investigate the corresponding direct problem as well. We establish the estimates for the norms of solutions to the nonlinear direct problem through the norms of solutions to the corresponding linear direct problem. This allow us to estimate the accuracy of the approximate solution and prove the order-optimality for the method of auxiliary boundary conditions.