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Mathematical model for ice formation in the Arctic during summer

By Alain Pham, Ngoc Dinh and Phan Thanh Nam

Abstract

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

Topics: false-bottoms, free boundaries problem, contraction principle
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