Complete quenching phenomenon for a parabolic p-Laplacian equation with a weighted absorption

摘要

Throughout this paper, we mainly consider the parabolic p-Laplacian equation with a weighted absorption ut − div(|∇u|^p−2∇u) = −λ|x|^αχ{u0}u^−β in a bounded domain Ω ⊆ ℝⁿ (n ≥ 1) with Lipschitz continuous boundary subject to homogeneous Dirichlet boundary condition. Here λ  0 and α  −n are parameters, and β ∈ (0, 1) is a given constant. Under the assumptions u0∈W01,p(Ω)∩L∞(Ω), u0 ≥ 0 a.e. in Ω, we can establish conditions of local and global in time existence of nonnegative solutions, and show that every global solution completely quenches in finite time a.e. in Ω. Moreover, we give some numerical experiments to illustrate the theoretical results.