Sidenko N. R.
Ukr. Mat. Zh. - 2006. - 58, № 2. - pp. 236–249
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 $ℝ^n,\; n ≥ 3$, 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.
Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 525–538
Asymptotics of solutions of a time-periodic boundary-value problem for a singularly perturbed nonlinear parabolic equation with rapidly oscillating coefficients
Ukr. Mat. Zh. - 1984. - 36, № 2. - pp. 165 - 171
Averaging of a boundary-value problem, periodic with respect to time, for a singularly perturbed weakly nonlinear parabolic equation
Ukr. Mat. Zh. - 1983. - 35, № 4. - pp. 441—447
Ukr. Mat. Zh. - 1973. - 25, № 4. - pp. 492—501