<p style='text-indent:20px;'>We consider the problem of recovering initial condition in one-dimensional one-phase Stefan for heat equation from knowledge position melting point. We first recall some properties free boundary solution. Then we study uniqueness and stability inversion. The principal contribution paper is a new logarithmic type estimate that shows inversion may be severely il...

We argue that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics up to now, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii's ideas for numerical solution of the problem is developed. Mathematical modelling of energy relaxation of some processes useful in modern ion beam technologies i...

Keywords: Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation a b s t r a c t We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the he...

We claim that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii ideas for numerical solution of the problem is developed. Mathematical modelling of energy relaxation of some processes useful in modern ion beam technologies is fulfilled....