Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation
2014 ◽
Vol 144
(3)
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pp. 557-566
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Keyword(s):
We study the asymptotic behaviour, as t → ∞, of the solutions to the nonlinear evolution equationwhere ΔpNu = Δu + (p−2) (D2u(Du/∣Du∣)) · (Du/∣Du∣) is the normalized p-Laplace equation and p ≥ 2. We show that if u(x,t) is a viscosity solution to the above equation in a cylinder Ω × (0, ∞) with time-independent lateral boundary values, then it converges to the unique stationary solution h as t → ∞. Moreover, we provide an estimate for the decay rate of maxx∈Ω∣u(x,t) − h(x)∣.
2012 ◽
Vol 45
(6)
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pp. 846-852
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2010 ◽
Vol 216
(7)
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pp. 2137-2144
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Keyword(s):
2021 ◽
2007 ◽
Vol 09
(02)
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pp. 217-251
Keyword(s):