Supercritical semilinear wave equation with non-negative potential

Vladimir Simeonov Gueorguiev, Charlotte Heiming, Hideo Kubo

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 languageEnglish
Pages (from-to)2267-2303
Number of pages37
JournalCommunications in Partial Differential Equations
Volume26
Issue number11-12
Publication statusPublished - 2001
Externally publishedYes

Fingerprint

Semilinear Wave Equation
Wave equations
Non-negative
Generalized Fourier Transform
Laplace Operator
Estimate
Mathematical operators
Wave equation
Linear equation
Fourier transforms

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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

In: Communications in Partial Differential Equations, Vol. 26, No. 11-12, 2001, p. 2267-2303.

Research output: Contribution to journalArticle

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