Open Access Research Article

Extinction and Decay Estimates of Solutions for a Class of Porous Medium Equations

Wenjun Liu12*, Mingxin Wang1 and Bin Wu2

Author Affiliations

1 Department of Mathematics, Southeast University, Nanjing 210096, China

2 College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China

For all author emails, please log on.

Journal of Inequalities and Applications 2007, 2007:087650  doi:10.1155/2007/87650


The electronic version of this article is the complete one and can be found online at: http://www.journalofinequalitiesandapplications.com/content/2007/1/087650


Received: 3 April 2007
Accepted: 6 September 2007
Published: 5 November 2007

© 2007 Liu et al.

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.

The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem of the porous medium equation , is studied. Sufficient conditions about the extinction and decay estimates of solutions are obtained by using -integral model estimate methods and two crucial lemmas on differential inequality.

References

  1. Ferreira, R, Vazquez, JL: Extinction behaviour for fast diffusion equations with absorption. Nonlinear Analysis: Theory, Methods & Applications. 43(8), 943–985 (2001). PubMed Abstract | Publisher Full Text OpenURL

  2. Leoni, G: A very singular solution for the porous media equation when . Journal of Differential Equations. 132(2), 353–376 (1996). Publisher Full Text OpenURL

  3. Peletier, LA, Zhao, JN: Source-type solutions of the porous media equation with absorption: the fast diffusion case. Nonlinear Analysis: Theory, Methods & Applications. 14(2), 107–121 (1990). PubMed Abstract | Publisher Full Text OpenURL

  4. Li, Y, Wu, J: Extinction for fast diffusion equations with nonlinear sources. Electronic Journal of Differential Equations. 2005(23), 1–7 (2005)

  5. Anderson, JR: Local existence and uniqueness of solutions of degenerate parabolic equations. Communications in Partial Differential Equations. 16(1), 105–143 (1991). Publisher Full Text OpenURL

  6. Anderson, JR: Necessary and sufficient conditions for the unique solvability of a nonlinear reaction-diffusion model. Journal of Mathematical Analysis and Applications. 228(2), 483–494 (1998). Publisher Full Text OpenURL

  7. Chen, SL: The extinction behavior of the solutions for a class of reaction-diffusion equations. Applied Mathematics and Mechanics. 22(11), 1352–1356 (2001)

  8. Chen, SL: The extinction behavior of solutions for a reaction-diffusion equation. Journal of Mathematical Research and Exposition. 18(4), 583–586 (1998)

  9. Liu, W: Periodic solutions of evolution -laplacian equations with a nonlinear convection term. International Journal of Mathematics and Mathematical Sciences. 2007, 10 pages (2007)