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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On some solutions to the Klein-Gordon equation related to an integral of Sonine


Author: Stuart Nelson
Journal: Trans. Amer. Math. Soc. 154 (1971), 227-237
MSC: Primary 35C15; Secondary 35Q99
DOI: https://doi.org/10.1090/S0002-9947-1971-0415049-9
MathSciNet review: 0415049
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Abstract: An integral due to Sonine is used to obtain an expansion for special solutions $ W(x,t)$ of the Klein-Gordon equation. This expansion is used to estimate the $ {L_p}$ norms $ \left\Vert W( \cdot ,t)\right\Vert _p$ as $ t \to \infty $. These estimates yield results on the time decay of a fairly wide class of solutions to the Klein-Gordon equation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0415049-9
Keywords: Klein-Gordon equation, Cauchy problem, asymptotic behavior, estimate of $ {L_p}$ norms, Fourier transform, Sonine's discontinuous integral, Bessel functions
Article copyright: © Copyright 1971 American Mathematical Society