Ukrainian Mathematical Journal

, Volume 49, Issue 12, pp 1932–1937 | Cite as

Smooth solution of one boundary-value problem

  • N. H. Khoma
  • P. V. Tsynalko
Brief Communications

Abstract

We study the boundary value problem for the quasilinear equation u u − uxx=F[u, ut], u(x, 0)= u(x, π)=0, u(x+w, t)=u(x, t), x ε ®, t ε [0, π], and establish conditions under which a theorem on the uniqueness of a smooth solution is true.

Keywords

Periodic Solution Periodic Function Linear Problem Smooth Solution Hyperbolic Equation 

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References

  1. 1.
    Yu. A. Mitropol’skii and N. H. Khoma, “Periodic solutions of quasilinear hyperbolie equations of second order,” Ukr. Mat. Zh., 47, No. 10, 1370–1375 (1995).MathSciNetGoogle Scholar
  2. 2.
    N. H. Khoma, “The existence of a smooth solution of a boundary-value problem,” Ukr. Mat. Zh., 47, No. 12, 1717–1719 (1995).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • N. H. Khoma
    • 1
  • P. V. Tsynalko
    • 2
  1. 1.Ternopol Academy of National EconomyTernopol
  2. 2.Ternopol Pedagogic InstituteTernopol

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