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

Saïd Benachour, Simona M. Hapca, Philippe Laurençot

Research output: Contribution to journalArticle

17 Citations (Scopus)


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
Issue number3-4
Publication statusPublished - 2007


Cite this