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Cauchy problem for the generalised radially symmetric wave equation

Published online by Cambridge University Press:  26 February 2010

W. E. Williams
W. E. Williams
Affiliation:
Department of Applied Mathematics, The University, Liverpool, 3
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Extract

A solution is obtained by real variable methods for a Cauchy problem for the generalised radially symmetric wave equation. A solution of this problem has been given by Mackie [1] employing the contour integral methods developed by Copson [2] and Mackie [3] for a class of problems occurring in gas dynamics. The present approach employs a simple definite integral representation for the solution and reduces the problem to solving an Abel integral equation. The real variable approach avoids the unnecessary restriction of the initial data to be analytic and also avoids the difficulty encountered in the complex variable approach in continuing the solution across a characteristic. The solution is in fact obtained in a form valid everywhere in the region of interest.

Type
Research Article
Information
Mathematika , Volume 8 , Issue 1 , June 1961 , pp. 66 - 68
Copyright
Copyright © University College London 1961

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References

1.Mackie, A. G., Proc. Roy. Soc. A, 236 (1956), 265.Google Scholar
2.Copson, E. T., Proc. Roy. Soc. A, 216 (1953), 539.Google Scholar
3.Mackie, A. G., Proc. Camb. Phil. Soc., 50 (1954), 131.CrossRefGoogle Scholar
4.Weinstein, A., Proc. 5th Symposium App. Maths. (1954), 137.CrossRefGoogle Scholar