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

International Mathematics Research Notices (Impact Factor: 1.12). 07/2011; DOI: 10.1093/imrn/rnr237
Source: arXiv

ABSTRACT 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.

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