Regularization of a two-dimensional two-phase inverse Stefan problem

We consider the problem of determining the boundary value u(1)(x, 0, t), i.e. the time-space-dependent heat flux v(x, t) in the two-dimensional, two-phase Stefan problem in which u(1)(x, y, t) represents the temperature in the liquid zone for a prescribed surface z(x, t) separating the ice and the liquid. To regularize this ill-posed problem the system of linear Volterra integral equations obtained will be turned into a linear Volterra equation of the second kind associated with an equation of the convolution type for which error estimates will be derived. Numerical results are given.