On the dynamics of shallow ice sheets. Modelling and analysis

TL;DR

This paper develops a mathematical model for the evolution of shallow ice sheets, involving complex variational inequalities with nonlinearities, and constructs solutions using a finite difference scheme in time.

Contribution

It introduces a novel variational inequality model for shallow ice sheet dynamics with nonlinear features and provides a solution construction method via finite difference schemes.

Findings

Model captures key dynamics of shallow ice sheets.

Finite difference scheme effectively constructs solutions.

Provides a framework for analyzing nonlinear ice sheet evolution.

Abstract

We formulate a model describing the evolution of thickness in a shallow ice sheet lying over a lithosphere. The model is thus governed by a set of variational inequalities that involve nonlinearities in the time derivative and in the elliptic term. Solutions are constructed via a finite difference scheme in time.