Weighted decay estimate for the wave equation

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The work is devoted to the proof of a new L∞-L weighted estimate for the solution to the nonhomogeneous wave equation in (3 + l)-dimensional space-time. The weighted Sobolev spaces are associated with the generators of the Poincarégroup. The estimate obtained is applied to prove the global existence of a solution to a nonlinear system of wave and Klein-Gordon equations with small initial data.

Original languageEnglish
Pages (from-to)393-402
Number of pages10
JournalProceedings of the American Mathematical Society
Volume112
Issue number2
DOIs
Publication statusPublished - 1991
Externally publishedYes

Fingerprint

Sobolev spaces
Weighted Estimates
Weighted Sobolev Spaces
Decay Estimates
Klein-Gordon Equation
Wave equations
Global Existence
Nonlinear systems
Wave equation
Nonlinear Systems
Space-time
Generator
Estimate

Keywords

  • Decay estimate
  • Wave equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Weighted decay estimate for the wave equation. / Covachev, Valery; Gueorguiev, Vladimir Simeonov.

In: Proceedings of the American Mathematical Society, Vol. 112, No. 2, 1991, p. 393-402.

Research output: Contribution to journalArticle

@article{38bb129e2f39480faf0c1e40ca6cdada,
title = "Weighted decay estimate for the wave equation",
abstract = "The work is devoted to the proof of a new L∞-L weighted estimate for the solution to the nonhomogeneous wave equation in (3 + l)-dimensional space-time. The weighted Sobolev spaces are associated with the generators of the Poincar{\'e}group. The estimate obtained is applied to prove the global existence of a solution to a nonlinear system of wave and Klein-Gordon equations with small initial data.",
keywords = "Decay estimate, Wave equation",
author = "Valery Covachev and Gueorguiev, {Vladimir Simeonov}",
year = "1991",
doi = "10.1090/S0002-9939-1991-1055769-7",
language = "English",
volume = "112",
pages = "393--402",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "2",

}

TY - JOUR

T1 - Weighted decay estimate for the wave equation

AU - Covachev, Valery

AU - Gueorguiev, Vladimir Simeonov

PY - 1991

Y1 - 1991

N2 - The work is devoted to the proof of a new L∞-L weighted estimate for the solution to the nonhomogeneous wave equation in (3 + l)-dimensional space-time. The weighted Sobolev spaces are associated with the generators of the Poincarégroup. The estimate obtained is applied to prove the global existence of a solution to a nonlinear system of wave and Klein-Gordon equations with small initial data.

AB - The work is devoted to the proof of a new L∞-L weighted estimate for the solution to the nonhomogeneous wave equation in (3 + l)-dimensional space-time. The weighted Sobolev spaces are associated with the generators of the Poincarégroup. The estimate obtained is applied to prove the global existence of a solution to a nonlinear system of wave and Klein-Gordon equations with small initial data.

KW - Decay estimate

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=84968503798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968503798&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1991-1055769-7

DO - 10.1090/S0002-9939-1991-1055769-7

M3 - Article

VL - 112

SP - 393

EP - 402

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -