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Journal of Mathematical Sciences

, Volume 206, Issue 4, pp 341–347 | Cite as

Nonlinear Characteristic Problem for a Nonlinear Oscillation Equation

  • R. Bitsadze
Article

Abstract

In this paper, we proposes a nonlinear version of the characteristic problem for a nonlinear oscillation equation, which allows us to define a regular solution and its extension domain simultaneously. The structure of these domains up to the proximity of the points of degeneracy of degree of the equation is described.

Keywords

Characteristic Invariant Quasilinear Equation Characteristic Problem Extension Domain Nonlinear Version 
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.

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References

  1. 1.
    L. Bers, “Mathematical aspects of subsonic and transonic gas dynamics,” in: Surv. Appl. Math., 3, Wiley, New York (1958).Google Scholar
  2. 2.
    A. V. Bitsadze, Equations of Mixed Type [in Russian], Izd. Akad. Nauk SSSR, Moscow (1959).Google Scholar
  3. 3.
    A. V. Bitsadze, Some Classes of Partial Differential Equations, Adv. Stud. Contemp. Math., 4, Gordon and Breach, New York (1988).Google Scholar
  4. 4.
    R. G. Bitsadze, “General representation of the solutions of a quasilinear equation of a problem of nonlinear oscillations,” Soobshch. Akad. Nauk Gruz. SSR, 128, No. 3, 493–496 (1988).MathSciNetGoogle Scholar
  5. 5.
    J. Gvazava, “Some classes of quasilinear equations of mixed type,” Proc. A. Razmadze Math. Inst., 67 (1981).Google Scholar
  6. 6.
    E. Goursat, Lecons sur l’intégration des équations aux dérivées partielles du second ordre à deux variables indépendantes. Tome II: La méthode de Laplace. Les systèmes en involutions. La methode de M. Darboux. Les équations de la première classe. Transformations des équations du second ordre. Généralisations diverses. 2 Notes, Hermann, Paris (1898).Google Scholar
  7. 7.
    J. Hadamard, Leçons sur la propagation des ondes et les équations de lhydrodynamique, Hermann, Paris (1903).Google Scholar
  8. 8.
    S. Kumei and G. W. Bluman, “When nonlinear differential equations are equivalent to linear differential equations?” SIAM J. Appl. Math., 42, No. 5, 1157–1173 (1982).CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    F. Tricomi, Lezzioni sulle Equazioni a Derivate Parziale, Editrice Gheroni, Torino (1954).Google Scholar
  10. 10.
    E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Vols. I and II, Cambridge Univ. Press, Cambridge (1927).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Georgian Technical UniversityTbilisiGeorgia

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