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.
|Number of pages||21|
|Publication status||Published - 2007|
Benachour, S., Hapca, S. M., & Laurençot, P. (2007). Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions. Asymptotic Analysis, 51(3-4), 209-229. http://content.iospress.com/articles/asymptotic-analysis/asy802