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

Abstract

SUMMARYThis 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 k 1 on the coefficient k of the first-order term, and the critical Fujita exponent is a finite number when k is between k ∞ and k 1 , while the critical exponent does not exist when k k ∞ or k k 1 .

Critical Fujita exponents for a class of nonlinear convection-diffusion equations

“…Assume, for contradiction, that there existed a nontrivial nonincreasing solution 0 g ∈ C 2 (0, +∞) satisfying (21) to the ordinary differential equation (20). We first prove the conclusion under the following assertion:…”