Self-similar solutions of the porous medium equation in a half-space with a nonlinear boundary condition: existence and symmetry

We find existence of a nonnegative compactly supported solution of the problem Δu = uα in RN +, ∂u/∂ν = u on ∂RN +. Moreover, we prove that every nonnegative solution with finite energy is compactly supported and radially symmetric in the tangential variables.  2004 Elsevier Inc. All rights reserved