Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q(0) and the critical Fujita exponent q(c) for the problems considered, and show that q(0) = q(c) for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q(0) < q(c) for the one-dimensional case. (c) 2008 Elsevier Inc. All rights reserved.