An obstacle problem in glaciology

In this talk, we present a new model describing the evolution of the flow in a shallow ice sheet.

Since the ice sheet height is constrained not to be lower than the height of the underlying bedrock, the problem under consideration is an obstacle problem.

After carefully deriving the formulation of the model under consideration starting from the flow law devised by Glen in 1952, we establish the existence of solutions to this time-dependent obstacle problem.

The variational formulation we recover upon completing an asymptotic process consists of a set of doubly nonlinear parabolic variational inequalities posed over a non-empty, closed and convex subset of a suitable Bochner space. Differently from the standard theory, the evolutionary term will be – in general – as regular as a vector-valed measure in the sense of Dinculeanu.

These results are drawn from my recent joint work with Roger Temam (Indiana University).

Bio
https://ppiersan.pages.iu.edu