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 language | English |
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Pages (from-to) | 209-229 |
Number of pages | 21 |
Journal | Asymptotic Analysis |
Volume | 51 |
Issue number | 3-4 |
Publication status | Published - 2007 |