Resolvent estimates and the decay of the solution to the wave equation with potential

Vladimir Georgiev

Journées équations aux dérivées partielles (2001)

  • page 1-7
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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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): 1-7. <http://eudml.org/doc/93415>.

@article{Georgiev2001,
abstract = {We prove a weighted $L^\infty $ 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.},
author = {Georgiev, Vladimir},
journal = {Journées équations aux dérivées partielles},
keywords = {generalized Fourier transform; finite dependence domain argument; global small data solution; supercritical semilinear wave equations},
language = {eng},
pages = {1-7},
publisher = {Université de Nantes},
title = {Resolvent estimates and the decay of the solution to the wave equation with potential},
url = {http://eudml.org/doc/93415},
year = {2001},
}

TY - JOUR
AU - Georgiev, Vladimir
TI - Resolvent estimates and the decay of the solution to the wave equation with potential
JO - Journées équations aux dérivées partielles
PY - 2001
PB - Université de Nantes
SP - 1
EP - 7
AB - We prove a weighted $L^\infty $ 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.
LA - eng
KW - generalized Fourier transform; finite dependence domain argument; global small data solution; supercritical semilinear wave equations
UR - http://eudml.org/doc/93415
ER -

References

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