Ukrainian Mathematical Journal

, Volume 58, Issue 2, pp 263–279 | Cite as

Averaging of the Dirichlet problem for a special hyperbolic Kirchhoff equation

  • N. R. Sidenko


We prove a statement on the averaging of a hyperbolic initial-boundary-value problem in which the coefficient of the Laplace operator depends on the space L2-norm of the gradient of the solution. The existence of the solution of this problem was studied by Pokhozhaev. In a space domain in ℝn, n ≥ 3, we consider an arbitrary perforation whose asymptotic behavior in a sense of capacities is described by the Cioranesku-Murat hypothesis. The possibility of averaging is proved under the assumption of certain additional smoothness of the solutions of the limiting hyperbolic problem with a certain stationary capacitory potential.


DIRICHLET Problem Laplace Operator Smooth Boundary Radon Measure Lipschitz Boundary 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • N. R. Sidenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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