Critical exponent for wave equation with potential

Vladimir Georgiev; Charlotte Heiming; Hideo Kubo

Critical exponent for wave equation with potential

Vladimir Georgiev, Charlotte Heiming, Hideo Kubo

Research output: Contribution to journal › Article › peer-review

Abstract

We establish a weighted L^∞ estimate for the solution of the linear wave equation with a smooth positive potential depending only on space variables. This estimate is similar to F.John's estimates in ([9]) and enables one to prove existence of global small data solution for the corresponding semilinear wave equation with potential.

Original language	English
Pages (from-to)	103-127
Number of pages	25
Journal	Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume	31
Publication status	Published - 2000
Externally published	Yes

Keywords

Decay estimates
Global solution
Semilinear equation
Wave equation
Wave equation with potential

ASJC Scopus subject areas

Mathematics(all)

Cite this

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title = "Critical exponent for wave equation with potential",

abstract = "We establish a weighted L∞ estimate for the solution of the linear wave equation with a smooth positive potential depending only on space variables. This estimate is similar to F.John's estimates in ([9]) and enables one to prove existence of global small data solution for the corresponding semilinear wave equation with potential.",

keywords = "Decay estimates, Global solution, Semilinear equation, Wave equation, Wave equation with potential",

author = "Vladimir Georgiev and Charlotte Heiming and Hideo Kubo",

note = "Publisher Copyright: {\textcopyright} 2000 EUT Edizioni Universita di Trieste.",

year = "2000",

language = "English",

volume = "31",

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journal = "Rendiconti dell'Istituto di Matematica dell'Universita di Trieste",

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TY - JOUR

T1 - Critical exponent for wave equation with potential

AU - Georgiev, Vladimir

AU - Heiming, Charlotte

AU - Kubo, Hideo

PY - 2000

Y1 - 2000

N2 - We establish a weighted L∞ estimate for the solution of the linear wave equation with a smooth positive potential depending only on space variables. This estimate is similar to F.John's estimates in ([9]) and enables one to prove existence of global small data solution for the corresponding semilinear wave equation with potential.

AB - We establish a weighted L∞ estimate for the solution of the linear wave equation with a smooth positive potential depending only on space variables. This estimate is similar to F.John's estimates in ([9]) and enables one to prove existence of global small data solution for the corresponding semilinear wave equation with potential.

KW - Decay estimates

KW - Global solution

KW - Semilinear equation

KW - Wave equation

KW - Wave equation with potential

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M3 - Article

AN - SCOPUS:0012959521

SN - 0049-4704

VL - 31

SP - 103

EP - 127

JO - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

JF - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

ER -

Critical exponent for wave equation with potential

Abstract

Keywords

ASJC Scopus subject areas

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