Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 506857, 7 pages
http://dx.doi.org/10.1155/2011/506857
Research Article

On Degenerate Parabolic Equations

Department of Mathematics, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia

Received 31 March 2011; Accepted 28 July 2011

Academic Editor: Mihai Putinar

Copyright © 2011 Mohammed Kbiri Alaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. R. Esteban and J. L. Vázquez, “Homogeneous diffusion in R with power-like nonlinear diffusivity,” Archive for Rational Mechanics and Analysis, vol. 103, no. 1, pp. 39–80, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  2. W. Jäger and J. Kačur, “Solution of porous medium type systems by linear approximation schemes,” Numerische Mathematik, vol. 60, no. 3, pp. 407–427, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. Blanchard and G. A. Francfort, “A few results on a class of degenerate parabolic equations,” Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, vol. 18, no. 2, pp. 213–249, 1991. View at Google Scholar · View at Zentralblatt MATH
  4. H. Brézis and M. G. Crandall, “Uniqueness of solutions of the initial-value problem for utΔφ(u)=0,” Journal de Mathématiques Pures et Appliquées, vol. 58, no. 2, pp. 153–163, 1979. View at Google Scholar
  5. A. Damlamian, “Some results on the multi-phase Stefan problem,” Communications in Partial Differential Equations, vol. 2, no. 10, pp. 1017–1044, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. P. Bénilan, Equations d'evolution dans un espace de Banach quelconque et applications, these d'Etat, Orsay, France, 1972. View at Zentralblatt MATH
  7. J. Kačur, A. Handlovičová, and M. Kačurová, “Solution of nonlinear diffusion problems by linear approximation schemes,” SIAM Journal on Numerical Analysis, vol. 30, no. 6, pp. 1703–1722, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Carrillo, J. I. Díaz, and G. Gilardi, “The propagation of the free boundary of the solution of the dam problem and related problems,” Applicable Analysis, vol. 49, no. 3-4, pp. 255–276, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. Donaldson, “Inhomogeneous Orlicz-Sobolev spaces and nonlinear parabolic initial value problems,” Journal of Differential Equations, vol. 16, pp. 201–256, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Elmahi and D. Meskine, “Parabolic equations in Orlicz spaces,” Journal of the London Mathematical Society, vol. 72, no. 2, pp. 410–428, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Porretta, “Existence results for nonlinear parabolic equations via strong convergence of truncations,” Annali di Matematica Pura ed Applicata. Serie Quarta, vol. 177, pp. 143–172, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet