TY - JOUR T1 - Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources AU - Wang , Lusheng AU - Wang , Zejia JO - Communications in Mathematical Research VL - 2 SP - 97 EP - 104 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19092.html KW - exterior domain, critical global exponent, critical Fujita exponent, fast diffusion equation. AB -
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.