Cauchy's Problem in a Non-Linear Partial Differential Equation of Hyperbolic Type
Published online by Cambridge University Press: 24 October 2008
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
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.
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