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

Journées équations aux dérivées partielles (2001)

- page 1-7
- ISSN: 0752-0360

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topGeorgiev, 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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