Blow-up for p-Laplacian parabolic equations
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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.
CitationLi, Y., & Xie, C. (2003). Blow-up for p-Laplacian parabolic equations. Electronic Journal of Differential Equations, 2003(20), pp. 1-12.
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