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It appears that the inverse operator maps the unit ball of $L^2(\\Omega\\times (0,T))$ into a space of functions which at small (time and space) scales are close in $H^1$ norm to a functional space of dimension n. It follows that once one has solved these equations at least n times it is possible to homogenize them both in space and in time, reducing the number of operation counts necessary to obtain further solutions. In practice we show under a Cordes-type condition that the first order time derivatives and second order space derivatives of the solution of these operators with respect to caloric coordinates are in $L^2$ (instead of $H^{-1}$ with Euclidean coordinates). If the medium is time-independent, then it is sufficient to solve n times the associated elliptic equation in order to homogenize the parabolic equation.<\/jats:p>","DOI":"10.1137\/060670420","type":"journal-article","created":{"date-parts":[[2007,12,12]],"date-time":"2007-12-12T18:02:46Z","timestamp":1197482566000},"page":"1-36","source":"Crossref","is-referenced-by-count":28,"title":["Homogenization of Parabolic Equations with a Continuum of Space and Time Scales"],"prefix":"10.1137","volume":"46","author":[{"given":"Houman","family":"Owhadi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,12,12]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/030600655"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.1013"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02786556"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"G. 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