Spherically symmetric Stefan problem with the Gibbs-Thomson law at the moving boundary
Spherically symmetric Stefan problem with the Gibbs-Thomson law at the moving boundary
Abstract: "This paper deals with the spherically symmetric Stefan problem in three space dimensions. The melting temperature satisfies the Gibbs-Thomson law. The solution is obtained as a limit of solutions of similar problems containing a small additional kinetic term in the melting temperature. Under some structural assumptions we show that the phase- change boundary has at most one discontinuity point t=T₀ (see the corresponding result for the planar Stefan problem in the paper of Götz & Zaltzman (1992)). In the one-phase problem the discontinuity point always exists. At the time T₀ the whole solid phase melts instantaneously. We study also the asymptotical stability (t -> [infinity]) of stationary solutions satisfying boundary conditions of thermostat type."