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# Séminaire de Physique Mathématique - EDP

Le 27 mars 2018
à 14:00
*Salle 2*
David Henry (Cork University)
**Prediction of the free-surface elevation for rotational water waves using the recovery of pressure at the bed**
In this talk we consider the pressure-streamfunction relationship for two-dimensional water waves which may possess an arbitrary distribution of vorticity. This question represents a highly-complex, intractable mathematical problem which also has immediate practical applications to both nearshore and offshore ocean environments. In the particular setting of linear waves, we provide a description of the role which the pressure function on the sea-bed plays in determining the free-surface profile elevation: the so-called free-surface profile recovery problem.Our approach is shown to provide a good approximation for a range of current conditions, leading to the derivation of expressions for the pressure transfer function, and the related pressure amplification factor, which generalise the well-known formulae for irrotational waves. An implementation of the moderate current approximation renders these expressions more tractable, leading to quite elegant and explicit formulae. This is joint work with Gareth Thomas (UCC).

Le 3 avril 2018
à 14:00
*Salle 2*
Eric Soccorsi (Centre de Physique Théorique, Marseille)

Le 10 avril 2018
à 14:00
*Salle 2*
Luchezar Stoyanov (University of Western Australia)
**On inverse scattering by obstacles**
We will discuss some problems related to recovering information about an obstacle K inan Euclidean space from certain measurements of lengths of generalized geodesics in the exteriorof the obstacle - e.g. sojourn times of scattering rays in the exterior of the obstacle, or simply travellingtimes of geodesics within a certain large ball containing the obstacle. It is well-known in scattering theorythat this scattering data is related to the singularities of the scattering kernel of the scatteringoperator for the wave equation in the exterior of K with Dirichlet boundary condition on the boundary.It turns out that for some classes of obstacles, K can be completely recovered from the scattering data- we will describe some types of obstacles with this property. On the other hand, in general, obstaclescannot be completely recovered from scattering data. The impediment in such cases is the set of trappedpoints - when this set is too large, observability of the obstacle is impossible. We will discuss certainstability property of the trapping set - it turns out that the measure of the set of trapped points dependscontinuously on perturbations of the obstacle K. We will derive this from a certain generalisation ofSantalo's formula to integrals over billiard trajectories (broken generalised geodesics) in the exteriorof an obstacle. Some other applications of this formula to scattering by obstacles will be discussed as well.

Le 24 avril 2018
à 14:00
*Salle 2*
Miguel Escobedo (Université du Pays Basque)

Le 5 juin 2018
à 14:00
*Salle 2*
Florent Berthelin (Université de Nice)

Responsable : Nicolas Popoff