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Annali di Matematica Pura ed Applicata

, Volume 89, Issue 1, pp 1–29 | Cite as

The singular Cauchy problem for a non-linear hyperbolic equation

  • Seymour Singer
Article
  • 18 Downloads

Summary

The author demonstrates the existence of a smooth solution to a singular initial value problem for a quasiliuear hyperbolic equation in two independent variables. The problem is transformed into an equivalent system of integral equations for which a solution is obtained by invoking Schauder’s fixed point theorem.

Keywords

Integral Equation Cauchy Problem Point Theorem Fixed Point Theorem Smooth Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    G. Birkhoff andG. Rota,Ordinary Differential Equations, Ginn, Boston, (1962).Google Scholar
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    W. Hurewicz,Lectures on Ordinary Differential Equations, MIT Press, Cambridge, Massachusetts, (1958).Google Scholar
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    D. Lick,A quasi-linear singular Cauchy problem, Annali di Mat.,74 (1966), 113–128.zbMATHMathSciNetGoogle Scholar
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    H. Ogawa,The singular Cauchy problem for a quasi linear hyperbolic equation of second order, J. Math. Mech.,12 (1963), 847–856.zbMATHMathSciNetGoogle Scholar
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    M. H. Protter,The Cauchy problem for a hyperbolic second order equation, Canad. J. Math.,6 (1954), 542–553.zbMATHMathSciNetGoogle Scholar
  6. [6]
    J. Schauder,Der Fixpunktsatz in Funktionalraumen, Studia Math.,2 (1930), 171–180.zbMATHGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • Seymour Singer
    • 1
  1. 1.USA

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