On uniqueness and iteration method of solving a non-linear non-stationary problem with non-local boundary conditions of “radiation heat transfer” type

The iterative process of solution of non-linear initial boundary problem with non-local boundary conditions is developed. In particular, such problems are widely used for modeling of radiation transfer processes. The constructed iterative process converges from any initial approximation. Uniqueness of the solution and convergence of the iterative process is proved under the conditions of existence of a smooth solution. The linear initial boundary problem with the third boundary condition is solved at each step of the iterative process. The rate of convergence of the iterative process is estimated and a priori estimates necessary for the iterative process are obtained.