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|Title: ||Decay estimates for a viscous Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions|
|Authors: ||Benachour, Saïd|
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|
|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.|
|Appears in Collections:||SIMBIOS Collection|
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