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American Mathematical Society, Proceedings of the American Mathematical Society, 2(112), p. 393-402, 1991

DOI: 10.1090/s0002-9939-1991-1055769-7

American Mathematical Society, Proceedings of the American Mathematical Society, 2(112), p. 393

DOI: 10.2307/2048732

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Weighted Decay Estimate for the Wave Equation

Journal article published in 1991 by Valery Covachev, Vladimir Georgiev ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

The work is devoted to the proof of a new L ∞ − L 2 {L^∞ } - {L^2} weighted estimate for the solution to the nonhomogeneous wave equation in ( 3 + 1 ) \left ( {3 + 1} \right ) -dimensional space-time. The weighted Sobolev spaces are associated with the generators of the Poincaré 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.