Numerical and analytical investigation of the free boundary confluence   for the phase field system
  In this paper we numerically research the solutions of the phase field system for the spherically symmetric Stefan-Gibbs-Thomson problem in the case of interaction of the free boundaries. We analyze the effect of the soliton type disturbance of the temperature in the point of the contact of the free boundaries. 
V.G. Danilov and V.Yu. Rudnev
math.AP