Geodesic
Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy
Izvestiya. Mathematics , Tome 41 (1993) no. 1, pp. 95-132

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The first part of this article is an investigation of the question of preservation of an exponential dichotomy for solutions of a linear parabolic equation upon a high-frequency perturbation of its principal terms. The second part contains a justification of the averaging principle on the whole time axis for quasilinear parabolic equations with rapidly oscillating principal part. 
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     author = {V. B. Levenshtam},
     title = {Averaging of quasilinear parabolic equations with rapidly oscillating principal part. {Exponential} dichotomy},
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V. B. Levenshtam. Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy. Izvestiya. Mathematics , Tome 41 (1993) no. 1, pp. 95-132. http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a4/