A Decay Estimate for a Wave Equation with Trapping and a Complex Potential

International Mathematics Research Notices (Impact Factor: 1.1). 07/2011; 2013(3). DOI: 10.1093/imrn/rnr237
Source: arXiv


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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