Affiliations: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Pl. 4, 125047 Moscow, Russia | Computer and Automation Institute, Hungarian Academy of Sciences, H-1502 Budapest P.O. Box 63, XI. Kende U. 13-17, Hungary | Departamento de Matemáticas, Univ. Autónoma de Madrid, 28049 Madrid, Spain
Note: [] Correspondence to: J.L. Vazquez, Departamento de Matemáticas, Univ. Autónoma de Madrid, 28049 Madrid, Spain.
Abstract: We study the large-time behaviour of the solution to the mixed problem: ut=Δ(e−1/u) in Q=Ω×(0,∞), with u(x, t) = 0 for x∈∂Ω, t≥0 and u(x,0)∈L∞(Ω), u(x,0)≥0. Ω is a bounded domain with smooth boundary ∂Ω. We show that there exists a function F(x) > 0 in Ω such that as t→∞ t(log t)2e−1/u→F(x) uniformly in x∈Ω. The function F is uniquely determined as the solution of the problem: ΔF=−1 in Ω, F=0 on ∂Ω.
