Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

In this equation, the nonnegative self-similar solutions to the parabolic filtration-absorption equation

is studied.

The behavior of the solution depends on the parameter c.

(1) c < 1. We can transform the equation into the well-known porous medium equation,

with m=2-c.

(2) c=1

(3) 1<3/2

Any compactly supported initial data expands and decays to zero algebraically in time

(3) c=3/2

(4) c>3/2

The solution goes to zero in finite time

Questions:

1. Boundary condition on the interface
2. Approximation with strictly nonnegative initial data
3. Numerical approximations: why there are oscillations for the transformed equation (27) in the paper?

See http://www.xinkexue.com/space-604-do-blog-id-1762.html for some figures.