| Abstract: |
| In this talk, which is the result of a joint work of the speaker with Roger Temam (Indiana University), we will study a model describing the evolution of the thickness of a grounded shallow ice sheet. Since the thickness of the ice sheet is constrained to be nonnegative, the problem under consideration is an obstacle problem.
A rigorous modelling exercise shows that this model, which is time-dependent, is governed by a set of variational inequalities that involve nonlinearities in the time derivative and in the elliptic term.
In order to establish the existence of solutions for the time-dependent model we recovered, formally, upon completion of the aforementioned modelling exercise, we first depart from a penalized relaxation, and we show - by resorting to a discretization in time - that the corresponding relaxed problem admits at least one solution.
Secondly, by means of Dubinskii`s lemma and other new results and new inequalities, we extract compactness for the family of solutions of the relaxed problems and we show that this family of solutions converges to a solution of a doubly nonlinear parabolic variational inequality akin to the one that was recovered formally. |
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