Geometric optics expansions for linear hyperbolic boundary value problems and optimality of energy estimates for surface waves.

Antoine Benoit (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

In this article we are interested in energy estimates for initial boundary value problem when surface waves occur that is to say when the uniform Kreiss Lopatinskii condition fails in the elliptic region or in the mixed region. More precisely we construct rigorous geometric optics expansions for elliptic and mixed frequencies and we show using those expansions that the instability phenomenon is higher in the case of mixed frequencies even if the uniform Kreiss Lopatinskii condition does not fail on hyperbolic modes. As a consequence this result allow us to give a classification of weakly well posed initial boundary value problems according to the region where the uniform Kreiss Lopatinskii condition degenerates.

Domaines: Equations aux dérivées partielles [math.AP]

Antoine Benoit. Geometric optics expansions for linear hyperbolic boundary value problems and optimality of energy estimates for surface waves.. Differential and integral equations, 2014, 27 (5/6), pp.531-562. ⟨hal-00801952⟩