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Please use this identifier to cite or link to this item: http://hdl.handle.net/10373/209

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Title: Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions
Authors: Benachour, Saïd
Dabuleanu-Hapca, Simona
Laurençot, Philippe
Hapca, Simona M.
Affiliation: University of Abertay Dundee. Scottish Informatics, Mathematics, Biology and Statistics Centre
Keywords: Hamilton-Jacobi equations
Issue Date: 2007
Publisher: IOS Press
Type: Journal Article
Refereed: peer-reviewed
Rights: Published version (c)IOS Press, available from http://iospress.metapress.com/content/q274j75645hj7422/?p=1a442d2cf01c4ccabdc535b5674ac685&pi=0
Citation: Benachour, S., Dăbuleanu-Hapca, S. and Laurençot, P. 2007. Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions. Asymptotic Analysis. 51(3-4): pp.209-229. [Online] Available from: http://iospress.metapress.com/content/q274j75645hj7422/?p=1a442d2cf01c4ccabdc535b5674ac685&pi=0
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.
URI: http://hdl.handle.net/10373/209
ISSN: 1875-8576
Appears in Collections:SIMBIOS Collection

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