On the dynamics of grounded shallow ice sheets: Modeling and analysis

• Published in: Advances in Nonlinear Analysis
• Main Authors: Piersanti Paolo, Temam Roger
• Format: Article in Journal/Newspaper
• Language: English
• Published: De Gruyter 2023
• Subjects: shallow ice approximation; doubly nonlinear equations; variational inequalities; penalty method; 35k61; 35k67; 35k86; 47h05; 86a40; Analysis; QA299.6-433; Ice Sheet
• Online Access: https://doi.org/10.1515/anona-2022-0280; https://doaj.org/article/56229a2d7812410c93b09f066904750b

In this article, we formulate a model describing the evolution of thickness of a grounded shallow ice sheet. The thickness of the ice sheet is constrained to be nonnegative. This renders the problem under consideration an obstacle problem. A rigorous analysis shows that the model is thus governed by a set of variational inequalities that involve nonlinearities in the time derivative and in the elliptic term, and that it admits solutions, whose existence is established by means of a semi-discrete scheme and the penalty method.