ON THE DYNAMICS OF SHALLOW ICE SHEETS. MODELLING AND ANALYSIS

• Main Authors: Piersanti, Paolo, Temam, Roger
• Other Authors: Karl-Franzens-Universität Graz
• Format: Report
• Language: English
• Published: HAL CCSD 2022
• Subjects: [MATH]Mathematics [math]; Ice Sheet
• Online Access: https://hal.archives-ouvertes.fr/hal-03613966; https://hal.archives-ouvertes.fr/hal-03613966/document; https://hal.archives-ouvertes.fr/hal-03613966/file/PT.pdf

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.