When we look at a differential equation in a very irregular media (composite material, mixed solutions, etc.) from very close, we may see a very complicated problem. However, if we look from far away we may not see the details and the problem may look simpler. The study of this effect in partial differential equations is known as homogenization. The effect of the inhomogeneities oscillating at small scales is often not a simple average and may be hard to predict: a geodesic in an irregular medium will try to avoid the bad areas, the roughness of a surface may affect in nontrivial way the shapes of drops laying on it, etc…
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Caffarelli, L., Silvestre, L. (2008). Issues in Homogenization for Problems with Non Divergence Structure. In: Dacorogna, B., Marcellini, P. (eds) Calculus of Variations and Nonlinear Partial Differential Equations. Lecture Notes in Mathematics, vol 1927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75914-0_2
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