### Abstract

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.

Original language | English |
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Pages (from-to) | 2267-2303 |

Number of pages | 37 |

Journal | Communications in Partial Differential Equations |

Volume | 26 |

Issue number | 11-12 |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Communications in Partial Differential Equations*,

*26*(11-12), 2267-2303.

**Supercritical semilinear wave equation with non-negative potential.** / Gueorguiev, Vladimir Simeonov; Heiming, Charlotte; Kubo, Hideo.

Research output: Contribution to journal › Article

*Communications in Partial Differential Equations*, vol. 26, no. 11-12, pp. 2267-2303.

}

TY - JOUR

T1 - Supercritical semilinear wave equation with non-negative potential

AU - Gueorguiev, Vladimir Simeonov

AU - Heiming, Charlotte

AU - Kubo, Hideo

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=10044223896&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10044223896&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 2267

EP - 2303

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 11-12

ER -