A decay estimate for a wave equation with trapping and a complex potential

Lars Andersson (1) , Pieter Blue (2) , Jean-Philippe Nicolas (3)

1 AEI - Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut )
2 School of Mathematics - University of Edinburgh
3 LM - Laboratoire de mathématiques de Brest

In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local energy decay) estimate. The equation is a model problem for certain scalar equations appearing in the Maxwell and linearised Einstein systems on the exterior of a rotating black hole.

Mots clés: Wave equation; trapping; complex potential; decay; Morawetz estimate

Domaines: Equations aux dérivées partielles [math.AP]

Lars Andersson, Pieter Blue, Jean-Philippe Nicolas. A decay estimate for a wave equation with trapping and a complex potential. 2011. ⟨hal-00612381⟩