Homogenization of Nonlinear Parabolic Operators of High Order
Homogenization of Nonlinear Parabolic Operators of High Order

Summary/Abstract: In this paper the behavior of the solution of the boundary value problem for nonlinear parabolic equations which elliptic part is periodical in time and in spatial variables. As in the linear case, in the current paper the correlation of the oscillations in time and spatial variables turns out to be important. This brings the formulation of five different cases which in analogy with the linear case are called time homogenization, spatial homogenization, self-similar homogenization and two cases of non-self-similar homogenization. In each of the above cases, the formulas for the calculation of the effective coefficients which define the homogenized equation are derived. The proved results are based on the G-convergence of the corresponding sequences of differential operators.

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