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Asymptotics of radiation fields in asymptotically Minkowski space

126   0   0.0 ( 0 )
 نشر من قبل Dean Baskin
 تاريخ النشر 2012
  مجال البحث
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We consider a non-trapping $n$-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation in all asymptotic regimes. The rates of decay seen in the asymptotic expansion are related to the resonances of a natural asymptotically hyperbolic problem on the northern cap of the compactification. For small perturbations of Minkowski space that fit into our framework, we show a rate of decay that improves on the Klainerman--Sobolev estimates.



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