(untitled) (Communications in Mathematical Research, 2021)
In this paper, we study the large time behavior of solutions to a class of fast 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 problem considered, and show that q_0 = q_c for the multi-dimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources, which is quite different from the known results that q_0 < q_c for the one-dimensional case; moreover, the value is different from the slow case.