Abstract: 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 consider ed 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 Fujita 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.

Key words: nonNewtonian filtration equation, critical Fujita ex ponent, threshold