Averaging of the Dirichlet problem for a special hyperbolic Kirchhoff equation
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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.
KeywordsDIRICHLET Problem Laplace Operator Smooth Boundary Radon Measure Lipschitz Boundary
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