Resolvent estimates and the decay of the solution to the wave equation with potential
Georgiev, Vladimir
Journées équations aux dérivées partielles, (2001), p. 1-7 / Harvested from Numdam
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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.

@article{JEDP_2001____A4_0,
     author = {Georgiev, Vladimir},
     title = {Resolvent estimates and the decay of the solution to the wave equation with potential},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2001},
     pages = {1-7},
     doi = {10.5802/jedp.588},
     mrnumber = {1843405},
     zbl = {1021.35071},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2001____A4_0}
}

Georgiev, Vladimir. Resolvent estimates and the decay of the solution to the wave equation with potential. Journées équations aux dérivées partielles,  (2001), pp. 1-7. doi : 10.5802/jedp.588. http://gdmltest.u-ga.fr/item/JEDP_2001____A4_0/

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