  The only source of ice formation in the Arctic during summer is a layer of
ice called false-bottoms between an under-ice melt pond and the underlying
ocean. Of interest is to give a mathematical model in order to determine the
simultaneous growth and ablation of false-bottoms, which is governed by both of
heat fluxes and salt fluxes. In one dimension, this problem may be considered
mathematically as a two-phase Stefan problem with two free boundaries. Our main
result is to prove the existence and uniqueness of the solution from the
initial condition.
