Critical Fujita exponents of degenerate and singular parabolic equations
Abstract:In this paper we investigate the critical Fujita exponent for the initial-value problem of the degenerate and singular nonlinear parabolic equation
|x|1 ∂u/∂t = Δum + |x|2up, x ∈ Rn, t > 0,
with a non-negative initial value, where p > m ≥ 1 and 0 ≤ 1 ≤ 2 < p(1 + 1) − 1. We prove that, for m < p ≤ pc = m + (2 + 2)/(n+1), every non-trivial solution blows up in finite time, while, for p > pc, there exist both global and non-global solutions to the problem.
Document Type: Research Article
Publication date: 2006-05-01