We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a (unique) solution that is analytic in space and time.

We consider a stochastic perturbation of the Stefan problem. The noise is Brownian in time and smoothly correlated in space. We prove existence and uniqueness and characterize the domain of existence.

This paper reformulates the two–phase solidification problem (i.e., the Stefan problem) as an inverse problem in which a cost functional is minimized with respect to the position of the interface and subject to PDE constraints. An advantage of this formulation is that it allows for a thermodynamically consistent treatment of the interface conditions in the presence of a contact point involving ...

We consider a new Stefan-type problem for the classical heat equation with latent and phase-change temperature depending of variable time. prove equivalence this Stefan class boundary value problems nonlinear canonical evolution involving source term two free boundaries. This is obtained by applying reduction to Burgers reciprocal-type transformations. Moreover, particular case, we obtain uniqu...