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
-
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
-
Leoni, G: A very singular solution for the porous media equation when . Journal of Differential Equations. 132(2), 353–376 (1996). Publisher Full Text
-
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
-
Li, Y, Wu, J: Extinction for fast diffusion equations with nonlinear sources. Electronic Journal of Differential Equations. 2005(23), 1–7 (2005)
-
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
-
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
-
Chen, SL: The extinction behavior of the solutions for a class of reaction-diffusion equations. Applied Mathematics and Mechanics. 22(11), 1352–1356 (2001)
-
Chen, SL: The extinction behavior of solutions for a reaction-diffusion equation. Journal of Mathematical Research and Exposition. 18(4), 583–586 (1998)
-
Liu, W: Periodic solutions of evolution -laplacian equations with a nonlinear convection term. International Journal of Mathematics and Mathematical Sciences. 2007, 10 pages (2007)