The hyperbolic region for hyperbolic boundary value problems

Jean-François Coulombel (1)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids

The well-posedness of hyperbolic initial boundary value problems is linked to the occurrence of zeros of the so-called Lopatinskii determinant. For an important class of problems, the Lopatinskii determinant vanishes in the hyperbolic region of the frequency domain and nowhere else. In this paper, we give a criterion that ensures that the hyperbolic region coincides with the projection of the forward cone. We give some examples of strictly hyperbolic operators that show that our criterion is sharp.

Mots clés: Hyperbolic region; Hyperbolic systems; boundary value problems

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Coulombel. The hyperbolic region for hyperbolic boundary value problems. Osaka Journal of Mathematics, 2011, 48 (2), pp.457-469. ⟨hal-00339526⟩