Self-similar solutions of the porous medium equation in a half-space with a nonlinear boundary condition
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Date
2004
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Abstract
We find existence of a nonnegative compactly supported solution of the problem Deltau = u(alpha) in R-+(N), partial derivativeu/partial derivativev = u on partial derivativeR(+)(N). Moreover, we prove that every nonnegative solution with finite energy is compactly supported and radially symmetric in the tangential variables. (C) 2004 Elsevier Inc. All rights reserved.
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Keywords
elliptic equations, nonlinear boundary conditions, symmetry