Existence and Uniqueness of Solution to the Two-Phase Stefan Problem with Convection

Abstract

The well posedness of the two-phase Stefan problem with convection is established in L 1 . First we consider the case with a singular enthalpy and we fix the convection velocity. In the second part of the paper we study the case of a smoothed enthalpy, but the convection velocity is the solution to a Navier-Stokes equation. In the last section we give some numerical illustrations of a physical case simulated using the models studied in the paper.

Nonlinear Fokker-Planck equation with reflecting boundary conditions

“…by using a similar approach with the one suggested in [4] [5] and [6]. To this purpose we define the function…”

“…where y 0 ∈ L 1 (O), we need to have D (A) = L 1 (O), but this follows by a similar argument as the one used in Theorem 2 from [4]. For reader's convenience we shall sketch it here.…”