Well-posedness of hyperbolic initial boundary value problems

Jean-François Coulombel (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

Assuming that a hyperbolic initial boundary value problem satsifies an a priori energy estimate with a loss of one tangential derivative, we show a well-posedness result in the sense of Hadamard. The coefficients are assumed to have only finite smoothness in view of applications to nonlinear problems. This shows that the weak Lopatinskii condition is roughly sufficient to ensure well-posedness in appropriate functional spaces.

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Coulombel. Well-posedness of hyperbolic initial boundary value problems. Journal de Mathématiques Pures et Appliquées, 2005, 84 (6), pp.786 - 818. ⟨10.1016/j.matpur.2004.10.005⟩. ⟨hal-01839021⟩