engleski

Reduction of dimension for parabolic equations via two-scale convergence

Inspired by the similar ideas from homogenization theory, in \cite{; ; ES}; ; we introduced the notion of two-scale convergence for thin domains that allow lower-dimensional approximations. We generalize that idea on evolutional spaces appearing in study of parabolic equations. We prove the compactness theorem, analogous to the one in stationary case. We apply our method to quasi-static lubrication problem.

Two-scale convergence ; thin domains ; parabolic equations ; lubrication ; Navier-Stokes system

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