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

Abstract

AbstractThis 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.