Mathematical model for ice formation in the Arctic during summer

• Main Authors: Alain Pham, Ngoc Dinh, Phan Thanh Nam
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: false-bottoms; free boundaries problem; contraction principle; Arctic
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.546.3296; http://hal.archives-ouvertes.fr/docs/00/29/73/25/PDF/False-bottoms-1.pdf

The only source of ice formation in the Arctic during summer is a layer of ice be-tween 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 unique-ness of the solution under suitable data.