{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:19Z","timestamp":1777447879655,"version":"3.51.4"},"reference-count":47,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2017,10,6]],"date-time":"2017-10-06T00:00:00Z","timestamp":1507248000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2017,10,6]]},"abstract":"<jats:p>\n                    We consider homogenization of a phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects. The pore-scale model consists of a strongly coupled system of time-dependent Stokes\u2013Cahn\u2013Hilliard equations. In the considered model the fluids are separated by an evolving diffuse interface of a finite width, which is assumed to be independent of the scale parameter\n                    <jats:italic toggle=\"yes\">\u03f5<\/jats:italic>\n                    . We obtain upscaled equations for the considered model by a rigorous two-scale convergence approach.\n                  <\/jats:p>","DOI":"10.3233\/asy-171436","type":"journal-article","created":{"date-parts":[[2017,10,6]],"date-time":"2017-10-06T11:37:16Z","timestamp":1507289836000},"page":"77-95","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["Homogenization of evolutionary Stokes\u2013Cahn\u2013Hilliard equations for two-phase porous media flow"],"prefix":"10.1177","volume":"105","author":[{"given":"\u013dubom\u00edr","family":"Ba\u0148as","sequence":"first","affiliation":[{"name":"Bielefeld University","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hari Shankar","family":"Mahato","sequence":"additional","affiliation":[{"name":"University of Georgia","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,10,6]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/130950136"},{"key":"e_1_3_2_3_2","doi-asserted-by":"crossref","unstructured":"H.\u00a0Abels Diffuse interface models for two-phase flows of viscous incompressible fluids PhD thesis Leipzig University 2007.","DOI":"10.4171\/ifb\/155"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/0523084"},{"key":"e_1_3_2_5_2","unstructured":"G.\u00a0Allaire Homogenization of the unsteady Stokes equations in porous media in: Progress in Partial Differential Equations: Calculus of Variations Applications Pont-\u00e0-Mousson 1991 Pitman Res. Notes Math. Ser. Vol.\u00a0267 Longman Sci. Tech. Harlow 1992 pp.\u00a0109\u2013123."},{"key":"e_1_3_2_6_2","unstructured":"G.\u00a0Allaire Two-scale convergence and homogenization of periodic structures Lecture Notes School on Homogenization ICTP Trieste 1993."},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fluid.30.1.139"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00134993"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2016048"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023084614058"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2007.2.529"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1017\/S095679250000053X"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-1999-345"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/100817942"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(02)02429-9"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1137\/080713148"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385847"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","unstructured":"K.R.\u00a0Daly and T.\u00a0Roose Homogenization of two fluid flow in porous media Proc. Roy. Soc. A: Math. Phys. Eng. Sci. 471(2176) (2015) 2014056-1\u20132014056-20. doi:10.1098\/rspa.2014.0564.","DOI":"10.1098\/rspa.2014.0564"},{"key":"e_1_3_2_19_2","unstructured":"S.\u00a0Dobbersch\u00fctz Homogenization techniques for lower dimensional structures Doctoral thesis University of Bremen Germany 2012."},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10665-010-9396-6"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-015-0778-y"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1137\/050638333"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.21136\/MB.2010.140831"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10492-012-0021-z"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1137\/09077059X"},{"key":"e_1_3_2_26_2","doi-asserted-by":"crossref","unstructured":"U.\u00a0Hornung (ed.) Homogenization and Porous Media Interdisciplinary Applied Mathematics Vol.\u00a06 Springer New York 1997.","DOI":"10.1007\/978-1-4612-1920-0"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6332"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2016.01.025"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.301110.040811a"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/hxw039"},{"key":"e_1_3_2_31_2","unstructured":"M.\u00a0Liero and S.\u00a0Reichelt Homogenization of Cahn\u2013Hilliard-type equations via evolutionary \u0393-convergence WIAS Preprint No. 2114 2015."},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500024276"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500030146"},{"issue":"1","key":"e_1_3_2_34_2","first-page":"35","article-title":"Two scale convergence","volume":"2","author":"Lukkassen D.","year":"2002","unstructured":"D.\u00a0Lukkassen, G.\u00a0Nguetseng and P.\u00a0Wall, Two scale convergence, International Journal of Pure and Applied Mathematics 2(1) (2002), 35\u201386.","journal-title":"International Journal of Pure and Applied Mathematics"},{"issue":"210","key":"e_1_3_2_35_2","first-page":"1","article-title":"Homogenization of a system of semilinear diffusion-reaction equations in an H1,p setting","volume":"2013","author":"Mahato H.S.","year":"2013","unstructured":"H.S.\u00a0Mahato and M.\u00a0B\u00f6hm, Homogenization of a system of semilinear diffusion-reaction equations in an H1,p setting, Electronic Journal of Differential Equations 2013(210) (2013), 1\u201322.","journal-title":"Electronic Journal of Differential Equations"},{"key":"e_1_3_2_36_2","unstructured":"M.\u00a0Neuss-Radu Homogenization techniques Diploma Thesis University of Heidelberg Germany 1992."},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1137\/0520043"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11242-011-9730-0"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.966"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1137\/070706410"},{"key":"e_1_3_2_41_2","unstructured":"M.\u00a0Schmuck and S.\u00a0Kalliadasis Rate of convergence of general phase field equations towards their homogenized limit 2017 https:\/\/arxiv.org\/abs\/1702.08292."},{"key":"e_1_3_2_42_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2012.0020"},{"key":"e_1_3_2_43_2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/26\/12\/3259"},{"key":"e_1_3_2_44_2","unstructured":"R.E.\u00a0Showalter Monotone Operators in Banach Space and Nonlinear Partial Differential Equations American Mathematical Society Providence RI 1997."},{"key":"e_1_3_2_45_2","doi-asserted-by":"publisher","DOI":"10.15764\/AM.2014.03003"},{"key":"e_1_3_2_46_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13370-016-0463-7"},{"key":"e_1_3_2_47_2","unstructured":"L.\u00a0Tartar The General Theory of Homogenization: A Personalized Introduction Springer Berlin 2009."},{"key":"e_1_3_2_48_2","unstructured":"R.\u00a0Temam Navier\u2013Stokes Equations: Theory and Numerical Analysis North-Holland Amsterdam 1977."}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-171436","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-171436","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-171436","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:06Z","timestamp":1777379766000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-171436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,6]]},"references-count":47,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2017,10,6]]}},"alternative-id":["10.3233\/ASY-171436"],"URL":"https:\/\/doi.org\/10.3233\/asy-171436","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,6]]}}}