ON THE DYNAMICS OF SHALLOW ICE SHEETS. MODELLING AND ANALYSIS

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 va...

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Bibliographic Details
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
Description
Summary: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.

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