Method of averaging for quasilinear parabolic equations with fast oscillating coefficients (Q1603061)

This paper is devoted to the method of averaging for the problem on (general) bounded solutions of quasilinear parabolic equations of an arbitrary order \(2k\) with the principal part fast oscillating with respect to time. Here the author studies this question when principal part is periodic in time. Under certain conditions on the stationary solution on \(W_0\) the author proves that \[ \| u_\omega-W_0\|_{C^{2k+\gamma, \gamma/2k}} \leq C\omega^{-1+\frac {\gamma}{2k}},\quad \gamma\in [0,1), C=\text{const}, \tag{1} \] where \(\omega\) is asymptotic parameter. In the paper the author also constructs higher approximations as well.