Ice formation in the Arctic during summer: false-bottoms

• Published in: Applied Mathematics and Computation
• Main Authors: Thanh Nam, Phan, Pham Ngoc Dinh, Alain, Hoang Quan, Pham, Duc Trong, Dang
• Other Authors: Mathematics Department (UNS-HCMC), University of Natural Sciences- HoChiMinhCity, Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), University of Natural Sciences- HoChiMinh City (UNS-HCMC), University of Natural Sciences- HoChiMinh City, Mathematics department, Sai Gon University, Ho Chi Minh city
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2014
• Subjects: False-bottoms; Free boundary problem; Green's function; Contraction Mapping Principle; 35R35; 35Q35; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; Arctic
• Online Access: https://hal.archives-ouvertes.fr/hal-00297325; https://hal.archives-ouvertes.fr/hal-00297325v2/document; https://hal.archives-ouvertes.fr/hal-00297325v2/file/False-bottom.pdf; https://doi.org/10.1016/j.amc.2013.11.003

22 pages International audience 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.