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Note on propagation of classical waves: I

Published online by Cambridge University Press:  24 October 2008

H. Kaneta
Affiliation:
Tokushima University, Japan

Extract

1. Consider the Cauchy problem for the classical wave equation in ℝn:

with initial conditions u(0, x) = uo(x) and ∂tu(0, x)= u1(x), where uj (j = 0,1) are compactly supported C∞ functions on ℝn. In this paper we shall establish the following result.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]John, F.. Plane Waves and Spherical Means (Springer-Verlag, 1955).Google Scholar
[2]Ludwig, D.. The Radon transform or Euclidean space. Comm. Pure and Appl. Math. 19 (1966), 4981.CrossRefGoogle Scholar
[3]Mizohata, S.. The Theory of Partial Differential Equations (Cambridge University Press, 1973).Google Scholar
[4]Watson, G. N.. A Treatise on the Theory of Bessel Functions (Cambridge University Press, 1922).Google Scholar