Critical Fujita exponents of degenerate and singular parabolic equations

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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 ≤ 12 < p(1 + 1) − 1. We prove that, for m < ppc = 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: May 1, 2006

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