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Cauchy's Problem in a Non-Linear Partial Differential Equation of Hyperbolic Type

Published online by Cambridge University Press:  24 October 2008

M. Raziuddin Siddiqi
M. Raziuddin Siddiqi*
Affiliation:
Fitzwilliam House
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Extract

Let p (x) be an essentially positive function defined in the interval 0 ≤ x ≤ π. We consider the non-linear partial differential equation

for the boundary conditions u (x, t) = 0,

for x = 0 and x = π,

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 2 , April 1935 , pp. 195 - 202
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

* Lichtenstein, L., “Zur Theorie partieller Differentialgleichungen zweiter Ordnung vom hyperbolischen Typus”, Journal für Math. 158 (1927), 80–91.Google Scholar

† Siddiqi, M. R., “On an infinite series of integrals involving Sturm-Liouville characteristic functions”. Bulletin Academy of Sciences, United Provinces (Allahabad), 3 (1934), 1–10.Google Scholar

‡ Lichtenstein, L., “Zur Analysis der unendlich vielen Variabeln”, Palermo Rendiconti, 38 (1914), 113–66.CrossRefGoogle Scholar

* Unless otherwise stated, the summation is to be taken from 1 to ∞ throughout this paper.

* L. Lichtenstein, loc. cit.

* M. R. Siddiqi, loc. cit.