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partial differential equations; homogenization; two-scale convergence; linear parabolic equations; oscillating coefficients in space and time variable; dissimilar speeds of oscillation; admissible test functions; corrector results; compactness result; interpolation; coefficients oscillating in space and time
We extend and complete some quite recent results by Nguetseng [Ngu1] and Allaire [All3] concerning two-scale convergence. In particular, a compactness result for a certain class of parameterdependent functions is proved and applied to perform an alternative homogenization procedure for linear parabolic equations with coefficients oscillating in both their space and time variables. For different speeds of oscillation in the time variable, this results in three cases. Further, we prove some corrector-type results and benefit from some interpolation properties of Sobolev spaces to identify regularity assumptions strong enough for such results to hold.
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