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 coupled system of parabolic/ODE equations describing solid combustion. For a given rescaling of the reaction term (the high activation energy limit), we show that the limit solution solves a free boundary problem which is to our knowledge new. In the time-increasing case, the limit coincides with the Stefan problem with spatially inhomogeneous coefficients. In general it is a para...

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 ...

Free Boundary Problems (FBP) motivated several studies in the past due to their relevance in applications [1 − 4]. From the mathematical point of view FBP are initial/ boundary value problems with a moving boundary [5]. The motion of the boundary is unknown (free boundary) and has to be determined together with the solution of the given partial differential equation. As a consequence the soluti...