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• W2964326595 abstract "Abstract We prove convergence of positive solutions to u t = u Δ u + u ∫ Ω | ∇ u | 2 , u | ∂ Ω = 0 , u ( ⋅ , 0 ) = u 0 in a bounded domain Ω ⊂ R n , n ≥ 1 , with smooth boundary in the case of ∫ Ω u 0 = 1 and identify the W 0 1 , 2 ( Ω ) -limit of u ( t ) as t → ∞ as the solution of the corresponding stationary problem. This behaviour is different from the cases of ∫ Ω u 0 1 and ∫ Ω u 0 > 1 which are known to result in convergence to zero or blow-up in finite time, respectively. The proof is based on a monotonicity property of ∫ Ω | ∇ u | 2 along trajectories and the analysis of an associated constrained minimization problem." @default.
• W2964326595 created "2019-07-30" @default.
• W2964326595 creator A5071892237 @default.
• W2964326595 date "2016-04-01" @default.
• W2964326595 modified "2023-10-01" @default.
• W2964326595 title "Equilibration of unit mass solutions to a degenerate parabolic equation with a nonlocal gradient nonlinearity" @default.
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• W2964326595 doi "https://doi.org/10.1016/j.na.2016.02.007" @default.
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