含内源与一阶项的非Newton渗流方程的临界指标

Critical Exponent for Non-Newtonian Filtration Equation with Interior Sources and One Order Term

研究含内源与一阶项的非Newton渗流方程齐次Neumann边值问题解的长时间渐近行为.证明了所研究问题的Fujita临界指标不但受空间维数和非线性指数的影响,还受方程中一阶项系数k的影响.证明了此问题一阶项系数k存在两个阈值k∞和k1(k∞<k1),使得当k∞<k<k1时,Fujita临界指标是一个取值大于1的有限实数,而当k≤k∞或k≥k1时,Fujita临界指标不存在.

This paper deals with the long time behavior of solutions to the homogeneous Neumann problem of the non-Newtonian filtration equation. It is shown that the critical Fujita exponent for the problem considered is determined not only by the spatial dimension and the nonlinearity exponent, but also by the coefficient k of the first order term. In fact, it is proved that there exist two thresholds k∞ and k1 on the coefficient k of the first order term, and the critical Filjita exponent is a finite number when k is between k∞ and k1, while the critical exponent does not exist when k≤k∞ or k≥k1.