Correctors for flow in a partially fissured medium.

Rajesh, M.

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Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data.

Chae, Dongho, Imanuvilov, Oleg Yu. (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Multiscale convergence and reiterated homogenization of parabolic problems

Anders Holmbom, Nils Svanstedt, Niklas Wellander (2005)

Applications of Mathematics

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Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_{ε} / \partial t - div (a (x, x / ε, x / ε^{2}, t, t / ε^{k}) \nabla u_{ε}) = f$ . It is shown that under standard assumptions on the function $a (x, y_{1}, y_{2}, t, τ)$ the sequence ${u_{ϵ}}$ of solutions converges weakly in $L^{2} (0, T; H_{0}^{1} (Ω))$ to the solution $u$ of the homogenized problem $\partial u / \partial t - div (b (x, t) \nabla u) = f$ .