{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:32:24Z","timestamp":1777447944555,"version":"3.51.4"},"reference-count":52,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T00:00:00Z","timestamp":1550016000000},"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":[[2019,2,13]]},"abstract":"<jats:p>Our aim in this paper is to study a modified higher-order (in space) phase field crystal model taking anisotropy into account. In particular, we deduce a priori estimates to prove well-posedness results and the dissipativity of the semigroup.<\/jats:p>","DOI":"10.3233\/asy-181494","type":"journal-article","created":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T10:19:46Z","timestamp":1550225986000},"page":"201-215","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Well-posedness for modified higher-order anisotropic Cahn\u2013Hilliard equations"],"prefix":"10.1177","volume":"111","author":[{"given":"Shuiran","family":"Peng","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et Applications, UMR CNRS 7348, Universit\u00e9 de Poitiers, Boulevard Marie et Pierre Curie\u00a0\u2013 T\u00e9l\u00e9port 2, F-86962 Chasseneuil Futuroscope Cedex, France. E-mail:\u00a0"}]},{"given":"Hongyi","family":"Zhu","sequence":"additional","affiliation":[{"name":"Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing, School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, China. E-mail:\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2019,2,13]]},"reference":[{"key":"ref001","unstructured":"S.\u00a0Agmon, Lectures on Elliptic Boundary Value Problems, Mathematical Studies, Van Nostrand, New York, 1965."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160120405"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160170104"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2011.4.311"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0001-6160(61)90182-1"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1063\/1.1744102"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.101111.110512a"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-011-0429-8"},{"issue":"1","key":"ref009","first-page":"39","volume":"7","author":"Cherfils L.","year":"2016","journal-title":"J. Appl. Anal. Comput."},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-40673-2_12"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1515\/anona-2016-0137"},{"key":"ref012","first-page":"1","volume":"9","author":"Cherfils L.","year":"2017","journal-title":"E. Jou. of Qualitative Theory of Differential Equations"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1007\/s00032-011-0165-4"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530513500243"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1063\/1.439809"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(94)00205-V"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1080\/00018732.2012.737555"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(01)00489-3"},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.79.051110"},{"key":"ref020","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.03.029"},{"key":"ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BF02181479"},{"key":"ref022","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139996313046"},{"key":"ref023","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.47.4289"},{"key":"ref024","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.47.4301"},{"key":"ref025","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2010.28.67"},{"key":"ref026","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2015092"},{"key":"ref027","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202514500365"},{"key":"ref028","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2015.35.2539"},{"key":"ref029","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.04.020"},{"key":"ref030","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90120-P"},{"key":"ref031","doi-asserted-by":"publisher","DOI":"10.1137\/100817590"},{"key":"ref032","doi-asserted-by":"publisher","DOI":"10.1137\/110834123"},{"key":"ref033","first-page":"141","volume":"12","author":"Miranville A.","year":"2014","journal-title":"Central Europ. J. Math."},{"key":"ref034","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2014.972384"},{"key":"ref035","doi-asserted-by":"publisher","DOI":"10.1002\/mma.3134"},{"key":"ref036","unstructured":"A.\u00a0Miranville, On the phase-field-crystal model with logarithmic nonlinear terms, RACSAM, to appear."},{"key":"ref037","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-5717(08)00003-0"},{"key":"ref038","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2010.28.275"},{"key":"ref039","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-5717(08)00004-2"},{"key":"ref040","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2011.10.1823"},{"key":"ref041","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2013.6.517"},{"key":"ref042","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.021606"},{"key":"ref043","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.225504"},{"key":"ref044","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.046107"},{"key":"ref045","doi-asserted-by":"publisher","DOI":"10.1016\/0956-7151(92)90091-R"},{"key":"ref046","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0645-3"},{"key":"ref047","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2008.0385"},{"key":"ref048","doi-asserted-by":"publisher","DOI":"10.4310\/MAA.2010.v17.n2.a4"},{"key":"ref049","doi-asserted-by":"publisher","DOI":"10.1137\/090752675"},{"key":"ref050","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1997.0086"},{"key":"ref051","doi-asserted-by":"publisher","DOI":"10.1137\/080738143"},{"key":"ref052","doi-asserted-by":"publisher","DOI":"10.4208\/jms.v51n3.18.02"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181494","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-181494","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-181494","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:36:21Z","timestamp":1777379781000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-181494"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,13]]},"references-count":52,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2019,2,13]]}},"alternative-id":["10.3233\/ASY-181494"],"URL":"https:\/\/doi.org\/10.3233\/asy-181494","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,13]]}}}