On Solutions to Nonlinear Reaction–Diffusion–Convection Equations with Degenerate Diffusion

Recent Results on Selfsimilar Solutions of Degenerate Nonlinear Diiusion Equations

On degenerate saturated-diffusion equations with convection

We study a class of degenerate parabolic convection–diffusion equations, endowed with a mechanism for saturation of the diffusion flux, which corrects the unphysical gradient-flux relations at high gradients. This paper extends our previous works on the effects of diffusion with saturation on convection and the impact of saturation on porous media-type diffusion, where it has been demonstrated ...

Nonlinear Degenerate Diffusion Problems

Self similar solutions u(x,t) = f(x//t) of the one-dimensional porousmedium equation are studied in this paper. These solutions emerge frominitial values that consist of two constant states: one non-positive forx < 0 and one non-negative for x > 0. With a diffusivity of the form|u| , we consider for m > 0 sign change solutions and for m e (-1,0]non-negative solutions. Th...

Radial equivalence for the two basic nonlinear degenerate diffusion equations

In this paper we prove that there exists an explicit correspondence between the radially symmetric solutions of two well-known models of nonlinear diffusion, the porous medium equation and the p-Laplacian equation. We establish exact correspondence formulas between these solutions. We also study in detail the application of the results in the important case of self-similar solutions. In particu...

L∞-Solutions for Some Nonlinear Degenerate Elliptic Equations

Correspondence should be addressed to Albo Carlos Cavalheiro, [email protected] Received 17 May 2011; Revised 6 October 2011; Accepted 6 October 2011 Academic Editor: Toka Diagana Copyright q 2011 Albo Carlos Cavalheiro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided...