Mathematics

 In this talk, we will review some recent results on the theory of obstacle problems in the context of elasticity and glaciology.
 
In the first part of the talk, which is the result of a collaboration with Philippe G. Ciarlet, we will review the justification of Koiter’s model for linearly elastic shells subjected to an obstacle in the case where the elastic shells are elliptic membranes or flexural shells. These results will be corroborated by a series of numerical experiments, whose genuineness hinges on some new augmentation of regularity results.
 
In the second part of the talk, which is the result of a collaboration with Roger Temam, we will review an existence theorem for a doubly-nonlinear parabolic variational inequality modelling the melting of a grounded shallow ice sheet.