Mathematical model for ice formation in the Arctic during summer
Résumé
The only source of ice formation in the Arctic during summer is a layer of ice between an under-ice melt pond and the underlying ocean, called false-bottoms. The simultaneous growth and ablation of false-bottoms is governed by both of heat fluxes and salt fluxes. This is a two-phase Stefan problem with two free boundaries. We first use Green functions to reduce this problem to solving a system of nonlinear integral equations, and then apply the contraction principle to prove the existence and uniqueness of the solution under suitable data.
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