ON THE DYNAMICS OF SHALLOW ICE SHEETS. MODELLING AND ANALYSIS

Paolo Piersanti (1) , Roger Temam

1 Karl-Franzens-Universität Graz

In this paper we formulate a model describing the evolution of thickness of a 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.

Domaines: Mathématiques [math]

Paolo Piersanti, Roger Temam. ON THE DYNAMICS OF SHALLOW ICE SHEETS. MODELLING AND ANALYSIS. 2022. ⟨hal-03613966⟩