Initial Velocity of the Emerging Free Boundary in a Two-Phase Stefan Problem with Imposed Flux

摘要

Consider the one-dimensional, two-phase Stefan Problem with an imposed flux in which the phase change front originates at the material boundary. We prove that, subject to suitable assumptions on the initial temperature and imposed flux, the initial speed of the phase change front is equal to the jump between the surface and initial fluxes at the boundary. Similarly, we prove that the front X(t) is continuously differentiable in the closed interval (0,t*) for some t* > 0. (ERA citation 10:007911)