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Uniqueness In Boundary Value Problems For The Second Order Hyperbolic Equation

Published online by Cambridge University Press:  20 November 2018

G. F. D. Duff
G. F. D. Duff*
Affiliation:
University of Toronto
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Introduction. We study linear normal hyperbolic partial differential equations of the second order, with one dependent variable u, and N independent variables xi (i = 1, … , N). The uniqueness theorem connected with the Cauchy problem for this type of equation is well known and in effect states that if u and its first normal derivatives vanish on a spacelike initial surface S then u vanishes in a certain conical region which contains S (1, p. 379).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 86 - 96
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Courant, R. and Hilbert, D., Methoden der Mathematischen Physik, 2 (Berlin, 1937).Google Scholar
2. Duff, G. F. D., Harmonic p-tensors on normal hyperbolic Riemannian spaces, Can. J. Math., 5 (1953), 57–80.Google Scholar
3. Duff, G. F. D., Partial Differential Equations (Toronto, 1956).Google Scholar
4. Hormander, L., Uniqueness theorems and estimates for normally hyperbolic partial differential, equations of the second order, C. R. Congres. Math. Scandinaves (1953), 105–115.Google Scholar
6. Synge, J. L. and Schild, A., Tensor Calculus (Toronto, 1949).Google Scholar