{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:53:46Z","timestamp":1758405226364,"version":"3.38.0"},"reference-count":21,"publisher":"SAGE Publications","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ASY"],"published-print":{"date-parts":[[2016,9,7]]},"DOI":"10.3233\/asy-161380","type":"journal-article","created":{"date-parts":[[2016,9,9]],"date-time":"2016-09-09T16:19:09Z","timestamp":1473437949000},"page":"183-205","source":"Crossref","is-referenced-by-count":8,"title":["From the viscous Cahn\u2013Hilliard equation to\u00a0a regularized forward-backward parabolic\u00a0equation"],"prefix":"10.1177","volume":"99","author":[{"given":"Pierluigi","family":"Colli","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica \u201cF. Casorati\u201d, Universit\u00e0 di Pavia, via Ferrata 1, 27100 Pavia, Italy. E-mail:\u00a0pierluigi.colli@unipv.it"}]},{"given":"Luca","family":"Scarpa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United\u00a0Kingdom. E-mail:\u00a0luca.scarpa.15@ucl.ac.uk"}]}],"member":"179","reference":[{"key":"10.3233\/ASY-161380_ref1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1088\/0951-7715\/8\/2\/002","article-title":"The viscous Cahn\u2013Hilliard equation. I. Computations","volume":"8","author":"Bai","year":"1995","journal-title":"Nonlinearity"},{"key":"10.3233\/ASY-161380_ref2","doi-asserted-by":"crossref","unstructured":"V.\u00a0Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976.","DOI":"10.1007\/978-94-010-1537-0"},{"key":"10.3233\/ASY-161380_ref4","unstructured":"H.\u00a0Brezis, Op\u00e9rateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Math. Stud., Vol.\u00a05, North-Holland, Amsterdam, 1973."},{"key":"10.3233\/ASY-161380_ref5","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1063\/1.1744102","article-title":"Free energy of a nonuniform system I. Interfacial free energy","volume":"2","author":"Cahn","year":"1958","journal-title":"J. Chem. Phys."},{"key":"10.3233\/ASY-161380_ref6","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s00032-011-0165-4","article-title":"The Cahn\u2013Hilliard equation with logarithmic potentials","volume":"79","author":"Cherfils","year":"2011","journal-title":"Milan J. Math."},{"key":"10.3233\/ASY-161380_ref7","doi-asserted-by":"crossref","first-page":"2696","DOI":"10.1137\/140984749","article-title":"Optimal boundary control of a viscous Cahn\u2013Hilliard system with dynamic boundary condition and double obstacle potentials","volume":"53","author":"Colli","year":"2015","journal-title":"SIAM J. Control Optim."},{"key":"10.3233\/ASY-161380_ref8","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1016\/j.jmaa.2015.04.057","article-title":"Cahn\u2013Hilliard equation with dynamic boundary conditions and mass constraint on the boundary","volume":"429","author":"Colli","year":"2015","journal-title":"J.\u00a0Math. Anal. Appl."},{"key":"10.3233\/ASY-161380_ref9","doi-asserted-by":"crossref","first-page":"6930","DOI":"10.1016\/j.jde.2016.01.032","article-title":"Nonlinear diffusion equations as asymptotic limits of Cahn\u2013Hilliard systems","volume":"260","author":"Colli","year":"2016","journal-title":"J. Differential Equations"},{"key":"10.3233\/ASY-161380_ref10","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1016\/j.jmaa.2014.05.008","article-title":"On the Cahn\u2013Hilliard equation with dynamic boundary conditions and a dominating boundary potential","volume":"419","author":"Colli","year":"2014","journal-title":"J. Math. Anal. Appl."},{"key":"10.3233\/ASY-161380_ref11","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1515\/anona-2015-0035","article-title":"A boundary control problem for the pure Cahn\u2013Hilliard equation with dynamic boundary conditions","volume":"4","author":"Colli","year":"2015","journal-title":"Adv. Nonlinear Anal."},{"key":"10.3233\/ASY-161380_ref12","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s00245-015-9299-z","article-title":"A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions","volume":"73","author":"Colli","year":"2016","journal-title":"Appl. Math. Optim."},{"key":"10.3233\/ASY-161380_ref13","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1137\/S0036141094267662","article-title":"On the Cahn\u2013Hilliard equation with degenerate mobility","volume":"27","author":"Elliott","year":"1996","journal-title":"SIAM J. Math. Anal."},{"key":"10.3233\/ASY-161380_ref14","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1006\/jdeq.1996.0101","article-title":"Viscous Cahn\u2013Hilliard equation. II","volume":"128","author":"Elliott","year":"1996","journal-title":"Analysis, J. Differential Equations"},{"key":"10.3233\/ASY-161380_ref15","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF00251803","article-title":"On the Cahn\u2013Hilliard equation","volume":"96","author":"Elliott","year":"1986","journal-title":"Arch. Rational Mech. Anal."},{"key":"10.3233\/ASY-161380_ref16","doi-asserted-by":"crossref","first-page":"881","DOI":"10.3934\/cpaa.2009.8.881","article-title":"On the Cahn\u2013Hilliard equation with irregular potentials and dynamic boundary conditions","volume":"8","author":"Gilardi","year":"2009","journal-title":"Commun. Pure Appl. Anal."},{"key":"10.3233\/ASY-161380_ref17","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1007\/s11401-010-0602-7","article-title":"Long-time behavior of the Cahn\u2013Hilliard equation with irregular potentials and dynamic boundary conditions","volume":"31","author":"Gilardi","year":"2010","journal-title":"Chin. Ann. Math. Ser. B"},{"key":"10.3233\/ASY-161380_ref18","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1137\/110824152","article-title":"Distributed optimal control of the Cahn\u2013Hilliard system including the case of a double-obstacle homogeneous free energy density","volume":"50","author":"Hinterm\u00fcller","year":"2012","journal-title":"SIAM J. Control Optim."},{"key":"10.3233\/ASY-161380_ref19","unstructured":"A.\u00a0Novick\u2013Cohen, On the viscous Cahn\u2013Hilliard equation, in: Material Instabilities in Continuum Mechanics (Edinburgh, 1985\u20131986), Oxford Sci. Publ., Oxford Univ. Press, New York, 1988, pp.\u00a0329\u2013342."},{"key":"10.3233\/ASY-161380_ref20","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1090\/S0002-9947-1991-1015926-7","article-title":"Stable patterns in a viscous diffusion equation","volume":"324","author":"Novick\u2013Cohen","year":"1991","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.3233\/ASY-161380_ref22","first-page":"19","article-title":"Optimal control of distributed parameter system given by Cahn\u2013Hilliard equation","volume":"19","author":"Wang","year":"2014","journal-title":"Nonlinear Funct. Anal. Appl."},{"key":"10.3233\/ASY-161380_ref23","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s10883-014-9259-y","article-title":"Optimal control problem for Cahn\u2013Hilliard equations with state constraint","volume":"21","author":"Zheng","year":"2015","journal-title":"J. Dyn. Control Syst."}],"container-title":["Asymptotic Analysis"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/ASY-161380","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T14:06:46Z","timestamp":1741615606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospress&doi=10.3233\/ASY-161380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,7]]},"references-count":21,"journal-issue":{"issue":"3-4"},"URL":"https:\/\/doi.org\/10.3233\/asy-161380","relation":{},"ISSN":["1875-8576","0921-7134"],"issn-type":[{"type":"electronic","value":"1875-8576"},{"type":"print","value":"0921-7134"}],"subject":[],"published":{"date-parts":[[2016,9,7]]}}}