Blow-up for p-Laplacian parabolic equations

Abstract

In this article we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem ut = ∇(|∇u|p-2 ∇u) + λ|u|q-2u, in ΩT, where p > 1. In particular, for p > 2, q = p is the blow-up critical exponent and we show that the sharp blow-up condition involves the first eigenvalue of the problem -∇(|∇ψ|p-2 ∇ψ) = λ|ψ|p-2ψ, in Ω; ψ|∂Ω = 0.