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)

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 languageEnglish
Pages (from-to)209-229
Number of pages21
JournalAsymptotic Analysis
Volume51
Issue number3-4
Publication statusPublished - 2007

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Decay Estimates
Hamilton-Jacobi Equation
Dirichlet Boundary Conditions
Extinction Time
Heat Semigroup
Global Classical Solution
Nonnegative Solution
Zero
Exponential Decay
Heat Equation
Linear equation
Converge

Cite this

Benachour, Saïd ; Hapca, Simona M. ; Laurençot, Philippe. / Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions. In: Asymptotic Analysis. 2007 ; Vol. 51, No. 3-4. pp. 209-229.
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Benachour, S, Hapca, SM & Laurençot, P 2007, 'Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions', 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.

In: Asymptotic Analysis, Vol. 51, No. 3-4, 2007, p. 209-229.

Research output: Contribution to journalArticle

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 -