{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:45:33Z","timestamp":1777448733170,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2009,2,1]],"date-time":"2009-02-01T00:00:00Z","timestamp":1233446400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2009,2]]},"abstract":"<jats:p>We investigate stochastic homogenization for some degenerate quasilinear parabolic PDEs. The underlying nonlinear operator degenerates along the space variable, uniformly in the nonlinear term: the degeneracy points correspond to the degeneracy points of a reference diffusion operator on the random medium.<\/jats:p>\n                  <jats:p>Assuming that this reference diffusion operator is ergodic, we can prove the homogenization property for the quasilinear PDEs, by means of the first-order approximation method. The (nonlinear) limit operator need not be nondegenerate. Concrete examples are provided.<\/jats:p>","DOI":"10.3233\/asy-2008-0925","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:04:15Z","timestamp":1575054255000},"page":"61-90","source":"Crossref","is-referenced-by-count":7,"title":["Stochastic homogenization of quasilinear PDEs with a spatial degeneracy"],"prefix":"10.1177","volume":"61","author":[{"given":"Fran\u00e7ois","family":"Delarue","sequence":"first","affiliation":[{"name":"LPMA, Universit\u00e9 Diderot Paris 7, UFR de Math\u00e9matiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France. E-mail: delarue@math.jussieu.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R\u00e9mi","family":"Rhodes","sequence":"additional","affiliation":[{"name":"CEREMADE, Universit\u00e9 Paris Dauphine, Place du marc\u00e9chal De Lattre de Tassigny, 75775 Paris Cedex 16, France. E-mail: rhodes@ceremade.dauphine.fr"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2009,2,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0925","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0925","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:38:48Z","timestamp":1777379928000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0925"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,2]]}},"alternative-id":["10.3233\/ASY-2008-0925"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0925","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2]]}}}