Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources

Abstract

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.