We apply a new version of multiscale convergence named very weak multiscale convergence to find possible frequencies of oscillation in an unknown coefficient of a partial differential equation from its solution. We also use this notion to study homogenization of a certain linear parabolic problem with multiple spatial and temporal scales.
Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂u ε ∂t − div a x ε , x ε 2 , t, Du ε = f . It is shown that under standard assumptions on the function a (y 1 , y 2 , t, ξ) the sequence {u ε } of solutions converges weakly in L p (0, T ; W 1, p 0 (Ω)) to the solution u of the homogenized problem ∂u ∂t − div (b (t, Du)) = f .
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