Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions

Saïd Benachour, Simona M. Hapca, Philippe Laurençot

    Research output: Contribution to journalArticlepeer-review

    19 Citations (Scopus)

    Abstract

    Global classical solutions to the viscous Hamilton–Jacobi equation ut−Δu=a|∇u|p in (0,∞)×Ω with homogeneous Dirichlet boundary conditions are shown to converge to zero in W1,∞(Ω) at the same speed as the linear heat semigroup when p>1. For p=1, an exponential decay to zero is also obtained but the rate depends on a and differs from that of the linear heat equation. Finally, if p∈(0,1) and a<0, finite time extinction occurs for non-negative solutions.
    Original languageEnglish
    Pages (from-to)209-229
    Number of pages21
    JournalAsymptotic Analysis
    Volume51
    Issue number3-4
    Publication statusPublished - 2007

    Keywords

    • Hamilton-Jacobi equations

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