{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:05:57Z","timestamp":1761807957288},"reference-count":23,"publisher":"EDP Sciences","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ESAIM: M2AN"],"published-print":{"date-parts":[[2016,7]]},"DOI":"10.1051\/m2an\/2015063","type":"journal-article","created":{"date-parts":[[2015,9,14]],"date-time":"2015-09-14T06:37:49Z","timestamp":1442212669000},"page":"1011-1033","source":"Crossref","is-referenced-by-count":12,"title":["An explicit finite-difference scheme for one-dimensional Generalized Porous Medium Equations: Interface tracking and the hole filling problem"],"prefix":"10.1051","volume":"50","author":[{"given":"L\u00e9onard","family":"Monsaingeon","sequence":"first","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2016,6,16]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems.Oxford Math. Monogr.Clarendon Press, Oxford, New York (2000).","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Aronson D.G., Regularity properties of flows through porous media: The interface.Arch. Rational Mech. Anal.37(1970) 1\u201310.","DOI":"10.1007\/BF00249496"},{"key":"R3","unstructured":"Aronson D.G., Regularity propeties of flows through porous media.SIAM J. Appl. Math.17(1969) 461\u2013467."},{"key":"R4","unstructured":"Aronson D.G. and B\u00e9nilan P., R\u00e9gularit\u00e9 des solutions de l\u2019\u00e9quation des milieux poreux dansRN.C. R. Acad. Sci. Paris S\u00e9r. A-B288(1979) A103\u2013A105."},{"key":"R5","unstructured":"Caffarelli L.A., V\u00e1zquez J.L., and Wolanski N.I., Lipschitz continuity of solutions and interfaces of theN-dimensional porous medium equation.Indiana Univ. Math. J.36(1987) 373\u2013401."},{"key":"R6","unstructured":"Caffarelli L.A. and Wolanski N.,C1,\u03b1regularity of the free boundary for theN-dimensional porous media equation.Commun. Pure Appl. Math.43(1990) 885\u2013902."},{"key":"R7","unstructured":"Crandall M.G. and Pierre M., Regularizing effects forut=\u0394\u03d5(u).Trans. Amer. Math. Soc.274(1982) 159\u2013168."},{"key":"R8","doi-asserted-by":"crossref","unstructured":"Dahlberg B.E.J. and Kenig C.E., Nonnegative solutions of generalized porous medium equations.Rev. Mat. Iberoamericana2(1986) 267\u2013305.","DOI":"10.4171\/RMI\/34"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"P. Daskalopoulos and C.E. Kenig, Degenerate diffusions. Initial value problems and local regularity theory. Vol. 1 ofEMS Tracts Math.European Mathematical Society (EMS), Z\u00fcrich (2007).","DOI":"10.4171\/033"},{"key":"R10","unstructured":"Daskalopoulos P. and Rhee E., Free-boundary regularity for generalized porous medium equations.Commun. Pure Appl. Anal.2(2003) 481\u2013494."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"de Pablo A. and V\u00e1zquez J.L., Regularity of solutions and interfaces of a generalized porous medium equation inRN.Ann. Mat. Pura Appl.158(74) 51\u201374.","DOI":"10.1007\/BF01759299"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"F. del Teso and J.L. V\u00e1zquezn, Finite difference method for a general fractional porous medium equation. Preprint arXiv:1307.2474 (2013).","DOI":"10.1007\/s10092-013-0103-7"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"E. DiBenedetto, Degenerate parabolic equations.Universitext. Springer-Verlag, New York (1993).","DOI":"10.1007\/978-1-4612-0895-2"},{"key":"R14","unstructured":"DiBenedetto E. and Hoff D., An interface tracking algorithm for the porous medium equation.Trans. Amer. Math. Soc.284(1984) 463\u2013500."},{"key":"R15","doi-asserted-by":"crossref","unstructured":"Gilding B.H., H\u00f6lder continuity of solutions of parabolic equations.J. London Math. Soc.13(1976) 103\u2013106.","DOI":"10.1112\/jlms\/s2-13.1.103"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"Graveleau J.L. and Jamet P., A finite difference approach to some degenerate nonlinear parabolic equations.SIAM J. Appl. Math.20(223) 199\u2013223.","DOI":"10.1137\/0120027"},{"key":"R17","unstructured":"Hoff D., A linearly implicit finite-difference scheme for the one-dimensional porous medium equation.Math. Comput.45(1985) 23\u201333."},{"key":"R18","doi-asserted-by":"crossref","unstructured":"Nakaki T. and Tomoeda K., A finite difference scheme for some nonlinear diffusion equations in an absorbing medium: support splitting phenomena.SIAM J. Numer. Anal.40(2002) 945\u2013964.","DOI":"10.1137\/S0036142900380303"},{"key":"R19","unstructured":"Sacks P.E., Continuity of solutions of a singular parabolic equation.Nonlin. Anal.7(1983) 387\u2013409."},{"key":"R20","unstructured":"Tomoeda K. and Mimura M., Numerical approximations to interface curves for a porous media equation.Hiroshima Math. J.13(1983) 273\u2013294."},{"key":"R21","unstructured":"Tomoeda K., Numerically repeated support splitting and merging phenomena in a porous media equation with strong absorption.J. Math-Industry3(2011) 61\u201368."},{"key":"R22","unstructured":"J.L. V\u00e1zquez, The porous medium equation.Oxford Math. Monogr.The Clarendon Press, Oxford University Press, Oxford (2007). Mathematical theory."},{"key":"R23","doi-asserted-by":"crossref","unstructured":"Zhang Q. and Wu Z., Numerical simulation for porous medium equation by local discontinuous Galerkin finite element method.J. Sci. Comput.38(2009) 127\u2013148.","DOI":"10.1007\/s10915-008-9223-7"}],"container-title":["ESAIM: Mathematical Modelling and Numerical Analysis"],"original-title":[],"link":[{"URL":"http:\/\/www.esaim-m2an.org\/10.1051\/m2an\/2015063\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T03:09:55Z","timestamp":1718075395000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.esaim-m2an.org\/10.1051\/m2an\/2015063"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,16]]},"references-count":23,"journal-issue":{"issue":"4"},"alternative-id":["m2an150067"],"URL":"https:\/\/doi.org\/10.1051\/m2an\/2015063","relation":{},"ISSN":["0764-583X","1290-3841"],"issn-type":[{"value":"0764-583X","type":"print"},{"value":"1290-3841","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,16]]}}}