### Abstract

Original language | English |
---|---|

Pages (from-to) | 209-229 |

Number of pages | 21 |

Journal | Asymptotic Analysis |

Volume | 51 |

Issue number | 3-4 |

State | Published - 2007 |

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### Cite this

*Asymptotic Analysis*,

*51*(3-4), 209-229.

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*Asymptotic Analysis*, vol 51, no. 3-4, pp. 209-229.

**Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions.** / Benachour, Saïd; Hapca, Simona M.; Laurençot, Philippe.

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

T2 - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 3-4

ER -