Lower exponential strong well-posedness of hyperbolic boundary value problems in a strip

Antoine Benoit (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

In this article we are interested in the lower exponential strong well-posedness of hyperbolic boundary value problems set in the strip R d−1 × [0, 1]. We assume that each component of the boundary of the strip satisfies the so-called uniform Kreiss-Lopatinskii condition (which is the condition ensuring the lower exponential strong well-posedness of the boundary value problem in the half space) and we show that due to selfinteraction phenomenon, an extra condition has to be made to ensure the lower exponential strong well-posedness of the boundary value problem in the strip. This condition imposes that a selfinteracting wave in the strip can not be amplified by repetitive reflections against each component of the boundary. This condition is very analogous to the one imposed in [Osher, 1973] to study the problem in the quarter space. However, due to the simplicity of the phases generation process for the strip geometry (less phases are generated) and this condition involves matrices and not Fourier integral operators.

Domaines: Equations aux dérivées partielles [math.AP]

Antoine Benoit. Lower exponential strong well-posedness of hyperbolic boundary value problems in a strip. Indiana University Mathematics Journal, 2020, 69 (7), pp.2267-2323. ⟨10.1512/iumj.2020.69.8091⟩. ⟨hal-01713012⟩