We prove that classical C 1-solutions to phase transition problems, which include the two-phase Stefan problem, are smooth. The problem is reduced to a xed domain using von Mises variables. The estimates are obtained by frozen coeecients and new L p estimates for linear parabolic equations with dynamic boundary condition. Crucial ingredients are the observation that a certain function is a Four...

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...

In this paper the possibility of application of the Adomian decomposition method for solving the moving boundary problem is presented. As an example of the moving boundary problem we consider a one-phase Stefan problem with Neumann’s boundary condition. This problem consists of finding the distribution of temperature in the domain and position of the moving interface. The validity of the approa...