Weighted decay estimate for the wave equation

Valery Covachev; Vladimir Georgiev

doi:10.1090/S0002-9939-1991-1055769-7

Weighted decay estimate for the wave equation

Valery Covachev, Vladimir Georgiev

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

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 language	English
Pages (from-to)	393-402
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	112
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1991-1055769-7
Publication status	Published - 1991 Jun
Externally published	Yes

Keywords

Decay estimate
Wave equation

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-1991-1055769-7

Cite this

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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.",

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author = "Valery Covachev and Vladimir Georgiev",

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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

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Weighted decay estimate for the wave equation

Abstract

Keywords

ASJC Scopus subject areas

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