Free Access
Issue
ESAIM: M2AN
Volume 50, Number 4, July-August 2016
Page(s) 1011 - 1033
DOI https://doi.org/10.1051/m2an/2015063
Published online 16 June 2016
  1. L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Math. Monogr. Clarendon Press, Oxford, New York (2000). [Google Scholar]
  2. D.G. Aronson, Regularity properties of flows through porous media: The interface. Arch. Rational Mech. Anal. 37 (1970) 1–10. [CrossRef] [MathSciNet] [Google Scholar]
  3. D.G. Aronson, Regularity propeties of flows through porous media. SIAM J. Appl. Math. 17 (1969) 461–467. [CrossRef] [MathSciNet] [Google Scholar]
  4. D.G. Aronson and P. Bénilan, Régularité des solutions de l’équation des milieux poreux dans RN. C. R. Acad. Sci. Paris Sér. A-B 288 (1979) A103–A105. [Google Scholar]
  5. L.A. Caffarelli, J.L. Vázquez, and N.I. Wolanski, Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Indiana Univ. Math. J. 36 (1987) 373–401. [CrossRef] [MathSciNet] [Google Scholar]
  6. L.A. Caffarelli and N. Wolanski, C1 regularity of the free boundary for the N-dimensional porous media equation. Commun. Pure Appl. Math. 43 (1990) 885–902. [CrossRef] [Google Scholar]
  7. M.G. Crandall and M. Pierre, Regularizing effects for ut = Δϕ(u). Trans. Amer. Math. Soc. 274 (1982) 159–168. [MathSciNet] [Google Scholar]
  8. B.E.J. Dahlberg and C.E. Kenig, Nonnegative solutions of generalized porous medium equations. Rev. Mat. Iberoamericana 2 (1986) 267–305. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Daskalopoulos and C.E. Kenig, Degenerate diffusions. Initial value problems and local regularity theory. Vol. 1 of EMS Tracts Math. European Mathematical Society (EMS), Zürich (2007). [Google Scholar]
  10. P. Daskalopoulos and E. Rhee, Free-boundary regularity for generalized porous medium equations. Commun. Pure Appl. Anal. 2 (2003) 481–494. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. de Pablo and J.L. Vázquez, Regularity of solutions and interfaces of a generalized porous medium equation in RN. Ann. Mat. Pura Appl. 158 (74) 51–74. [Google Scholar]
  12. F. del Teso and J.L. Vázquezn, Finite difference method for a general fractional porous medium equation. Preprint arXiv:1307.2474 (2013). [Google Scholar]
  13. E. DiBenedetto, Degenerate parabolic equations. Universitext. Springer-Verlag, New York (1993). [Google Scholar]
  14. E. DiBenedetto and D. Hoff, An interface tracking algorithm for the porous medium equation. Trans. Amer. Math. Soc. 284 (1984) 463–500. [CrossRef] [MathSciNet] [Google Scholar]
  15. B.H. Gilding, Hölder continuity of solutions of parabolic equations. J. London Math. Soc. 13 (1976) 103–106. [CrossRef] [MathSciNet] [Google Scholar]
  16. J.L. Graveleau and P. Jamet, A finite difference approach to some degenerate nonlinear parabolic equations. SIAM J. Appl. Math. 20 (223) 199–223. [Google Scholar]
  17. D. Hoff, A linearly implicit finite-difference scheme for the one-dimensional porous medium equation. Math. Comput. 45 (1985) 23–33. [CrossRef] [Google Scholar]
  18. T. Nakaki and K. Tomoeda, A finite difference scheme for some nonlinear diffusion equations in an absorbing medium: support splitting phenomena. SIAM J. Numer. Anal. 40 (2002) 945–964. [CrossRef] [MathSciNet] [Google Scholar]
  19. P.E. Sacks, Continuity of solutions of a singular parabolic equation. Nonlin. Anal. 7 (1983) 387–409. [CrossRef] [Google Scholar]
  20. K. Tomoeda and M. Mimura, Numerical approximations to interface curves for a porous media equation. Hiroshima Math. J. 13 (1983) 273–294. [MathSciNet] [Google Scholar]
  21. K. Tomoeda, Numerically repeated support splitting and merging phenomena in a porous media equation with strong absorption. J. Math-Industry 3 (2011) 61–68. [Google Scholar]
  22. J.L. Vázquez, The porous medium equation. Oxford Math. Monogr. The Clarendon Press, Oxford University Press, Oxford (2007). Mathematical theory. [Google Scholar]
  23. Q. Zhang and Z. Wu, Numerical simulation for porous medium equation by local discontinuous Galerkin finite element method. J. Sci. Comput. 38 (2009) 127–148. [CrossRef] [MathSciNet] [Google Scholar]

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