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 q0 and the critical Fujita exponent qc for the problems considered, and show that q0=qc 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 q0