On critical Fujita exponents for the porous medium equation with a nonlinear boundary condition

We establish the critical Fujita exponents for the solution of the porous medium equation ut = Δum, x ∈ RN +, t > 0, subject to the nonlinear boundary condition −∂um/∂x1 = up, x1 = 0, t > 0, in multi-dimension.  2003 Elsevier Inc. All rights reserved.