Ukrainian Mathematical Journal

, Volume 56, Issue 12, pp 2007–2016 | Cite as

On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations

  • H. L. Kulinich
  • S. V. Kushnirenko


We consider a solution of the Cauchy problem u(t, x), t > 0, xR2, for one class of integro-differential equations. These equations have the following specific feature: the matrix of the coefficients of higher derivatives is degenerate for all x. We establish conditions for the existence of the limit limt→∞u(t, x) = v(x) and represent the solution of the Cauchy problem in explicit form in terms of the coefficients of the equation.


Cauchy Problem Explicit Form High Derivative 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • H. L. Kulinich
    • 1
  • S. V. Kushnirenko
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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