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Radiation fields and hyperbolic scattering theory

Published online by Cambridge University Press:  24 October 2008

F. G. Friedlander
F. G. Friedlander
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Extract

Let u(x, t), where x ∈ 3, t ∈ , be a C∞ solution of the wave equation on {|x| > a} × for some a > 0, and suppose that u = 0 for |x|> a, t < 0. One then also has u = 0 for |x| > a + t, t > 0, so that u(.,t) can be thought of as a wave expanding into a previously undisturbed medium. One can now ask for a description of the asymptotic behaviour of u as |x| → ∞. It turns out that there is a v0(θ, τ) ∈ C∞ (S2 × ) such that

in the topology of C∞ (S2 × ). This limit may be called the radiation field of the expanding wave u. (See (2) and the earlier papers quoted there.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 3 , November 1980 , pp. 483 - 515
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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