The Regularization Variational Method for Solving Inverse Stefan Problems

Abstract

In Chapter 1 we have considered the mathematical statements of boundary and coefficient inverse Stefan problems for the quasilinear parabolic equation with various additional information about their solution. In this connection the choice of the function spaces for the inverse tasks relies on the faithful differential relations in the Hölder spaces established in Chapter 4 between the input data and the solution of the corresponding direct Stefan problems. Now we propose the regularization variational method for obtaining approximate solutions of inverse Stefan problems in the chosen spaces. Results for stability of the regularized solutions in the usual, or some generalized, sense are established below.