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

Abstract

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.

Keywords

• shallow ice approximation
• doubly nonlinear equations
• variational inequalities
• penalty method
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