Geodesic
Resolvent estimates and the decay of the solution to the wave equation with potential
Journées équations aux dérivées partielles (2001), article no. 4, 7 p.
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We prove a weighted L ∞ estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.

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     author = {Georgiev, Vladimir},
     title = {Resolvent estimates and the decay of the solution to the wave equation with potential},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {4},
     pages = {1--7},
     year = {2001},
     publisher = {Universit\'e de Nantes},
     doi = {10.5802/jedp.588},
     mrnumber = {1843405},
     zbl = {1021.35071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.588/}
}
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Georgiev, Vladimir. Resolvent estimates and the decay of the solution to the wave equation with potential. Journées équations aux dérivées partielles (2001), article  no. 4, 7 p.. doi: 10.5802/jedp.588

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