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On a Theorem Of Le Roux

Published online by Cambridge University Press:  20 November 2018

J. B. Diaz
Affiliation:
Institute for Fluid Dynamics and Applied Mathematics University of Maryland
G. S. S. Ludford
Affiliation:
Department of Mathematics University of Maryland
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1. The Theorem of Le Roux. Let U(x, y, α) be any solution of the linear hyperbolic differential equation

1

containing a parameter α. J. Le Roux (5) has shown that the function u(x, y) defined by

2 α0 = const.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Bergmann, S., Zitr Theorie der Funktionen, die eine lineare partielle Differ entialgleichung befriedigen, Mathematischeskii Sbornik (NewSer.), 2 (1937), 11691198.Google Scholar
2. Darboux, G., Lecons sur la théorie gén rale des surfaces, 2 (2nd e-resized., Paris 1914-15).Google Scholar
3. Diaz, J. B. and Ludford, G. S. S., On two methods of generating solutions of linear partial differential equations by means of definite integrals, Quarterly Appl. Math., 12 (1955), 422–427; C. R. (Paris), 238 (1954), 19631964.Google Scholar
4. Hadamard, J., Lectures on Cauchy's Problem in Linear Partial Differential Equations (New York, 1952).Google Scholar
5. Le Roux, J., Sur les intégrales des équations linéaires aux derivées partielles du second ordre à deux variables indépendantes, Ann. de l'École Norm. Sup. (3), 12 (1895), 227316.Google Scholar
6. Weinstein, A., The generalized radiation problem and the Ruler-Poisson-Darboux equation, Summa Brasiliensis, to appear in 1955.Google Scholar