Critical exponent for non-Newtonian filtration equation with homogeneous Neumann boundary data

This paper is concerned with large 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, we show 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. Copyright © 2007 John Wiley & Sons, Ltd.