Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 209-229 |
| Number of pages | 21 |
| Journal | Asymptotic Analysis |
| Volume | 51 |
| Issue number | 3-4 |
| Publication status | Published - 2007 |
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Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions. / Benachour, Saïd; Hapca, Simona M.; Laurençot, Philippe.
In: Asymptotic Analysis, Vol. 51, No. 3-4, 2007, p. 209-229.Research output: Contribution to journal › Article
TY - JOUR
T1 - Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions
AU - Benachour, Saïd
AU - Hapca, Simona M.
AU - Laurençot, Philippe
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
M3 - Article
VL - 51
SP - 209
EP - 229
JO - Asymptotic Analysis
JF - Asymptotic Analysis
SN - 0921-7134
IS - 3-4
ER -