The asymptotic behavior of viscosity solutions to the Cauchy-Dirichlet problem for the degenerate parabolic equation u t = Δ∞ u in Ω × (0,∞), where Δ∞ stands for the so-called infinity-Laplacian, is studied in three cases: (i) Ω = R Nand the initial data has a compact support; (ii) Ω is bounded and the boundary condition is zero; (iii) Ω is bounded and the boundary condition is non-zero. Our method of proof is based on the comparison principle and barrier function arguments. Explicit representations of separable type and self-similar type of solutions are also established. Moreover, in case (iii), we propose another type of barrier function deeply related to a solution of Δφ = 0.
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