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Weighted decay estimate for the wave equation

Authors: Valéry Covachev and Vladimir Georgiev
Journal: Proc. Amer. Math. Soc. 112 (1991), 393-402
MSC: Primary 35L05; Secondary 35B45, 35Q40
MathSciNet review: 1055769
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Abstract: The work is devoted to the proof of a new $ {L^\infty } - {L^2}$ weighted estimate for the solution to the nonhomogeneous wave equation in $ \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.

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Keywords: Decay estimate, wave equation
Article copyright: © Copyright 1991 American Mathematical Society