Degenerate Diffusion in Heterogeneous Media
Abstract: In this talk, I will present some recent results on the long-time behavior of non-negative solutions to the Cauchy problem for the Porous Medium Equation in the presence of variable density vanishing at infinity, [RV], [KRV].
[RV] G. Reyes & J.L. Vázquez, Long time behavior for the inhomogeneous PME in a medium with slowly decaying density, Commun. Pure Appl. Anal. 8 (2) (2009), pp. 493-508.
[KRV] S. Kamin, G. Reyes & J.L. Vázquez, Long time behavior for the inhomogeneous PME in a medium with a rapidly decaying density, Discrete and Continuous Dynamical Systems, (special issue devoted to Nonlinear Parabolic Problems), DCDS-A 26 (2) (2010), pp. 521-549.