Averaging of the Dirichlet problem for a special hyperbolic Kirchhoff equation |
| |
Authors: | N R Sidenko |
| |
Institution: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev |
| |
Abstract: | 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 L
2-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.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 236–249, February, 2006. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|