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Further, we present results on the more delicate fourth\u2010order thin\u2010film equation for which a nonnegativity\u2010preserving scheme is derived. The dead core phenomenon is presented for the Hele\u2013Shaw cell.<\/jats:p>","DOI":"10.1137\/050628015","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:30:58Z","timestamp":1156433458000},"page":"1203-1227","source":"Crossref","is-referenced-by-count":39,"title":["Lagrangian Numerical Approximations to One\u2010Dimensional Convolution\u2010Diffusion Equations"],"prefix":"10.1137","volume":"28","author":[{"given":"Laurent","family":"Gosse","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giuseppe","family":"Toscani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1997310506151"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023032000560"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00379920"},{"key":"R4","first-page":"337","volume":"1","author":"Bernis F.","year":"1996","journal-title":"Adv. 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Pareschi,\n                      On the fast evaluation of kinetic equations for driven granular media\n                      , in Numerical Analysis and Advanced Applications\u2014Proceedings of ENUMATH 2001, The 4th Conference on Numerical Mathematics and Advanced Applications, Ischia, Italy, 2001, Springer\u2010Italia, Milan, 2003.","DOI":"10.1007\/978-88-470-2089-4_44"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2003.11.006"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2000127"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1007\/s00028-005-0183-1"},{"key":"R32","doi-asserted-by":"crossref","unstructured":"C. Villani,\n                      Topics in Optimal Mass Transportation\n                      , Grad. Stud. Math. 58. 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