PhD grants : Geometrical quantity and observability (MIPTIS)

• Keywords

observability, wave equation, probabilities

• Profile and skills required

  Master 2 of fundamental mathematics : a good knowledge of classical analytic tools

• Project description

  The goal of this thesis is to generalize some results by E. Humbert, Y. Privat et E. Trélat on the geometrical constant which naturally appears when we make some measure of the energy of a wave on a domain which is smaller than the domain of propagation of the wave. This constant is defined as the minimum over the set of geodesics of the time spent in the observation domain within a fixed time interval. These results were devoted to the computation of this constant when the wave propagates on a flat torus and when the observation domain is a union of small squares, of size 1/n, which are randomly put in the observation domain with probability p. The main result was that this constant converges in probability towards pT. The goal of this thesis is to generalize this result in all dimensions and/or to the case where the wave propagates on an arbitrary compact Riemannian manifold.

• References

  E. Humbert, Y. Privat, E. Trélat : Geometric and probabilistic results for the

  observability of the wave equation, Preprint 2019 hal-01652890v2.

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