Solving an ill-posed problem for a nonlinear differential equation by means of the projection regularization method

The article investigates a problem with inverse time for a semilinear parabolic equation equipped with nonlocal boundary conditions. The problem under study arises, for example, in the mathematical modeling of the process of external gettering of silicon wafers in the creation of semiconductor devices. At the same time, when developing a mathematical model in the case of a high-intensive diffusion process, it is necessary to take into account the effects associated with the nonlinearity of the process. The paper suggests an approach for constructing a numerical solution to the problem with the inverse time, stable with respect to small perturbations of the initial data. The numerical solution is constructed using the regularization method based on adding a term with a small parameter to the overdetermination (final) condition. To obtain an approximate solution, the problem statement must recon in supplementary (a priori) information characterizing the exact solution. We obtain an error estimate for the approximate solution under the given a priori information.