Decay Estimates for a Viscous Hamilton-Jacobi Equation with Homogenious Dirichet Boundary Conditions

Details Decay Estimates for a Viscous Hamilton-Jacobi Equation with Homogenious Dirichet Boundary Conditions Decay Estimates for a Viscous Hamilton-Jacobi Equation with Homogenious Dirichet Boundary Conditions

2006-09-12

arxiv.org/abs/math/0609332v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

Global classical solutions to the viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions are shown to converge to zero at the same speed as the linear heat semigroup when p > 1. For p = 1, an exponential decay to zero is also obtained in one space dimension but the rate depends on a and differs from that of the linear heat equation. Finally, if 0 < p < 1 and a < 0, finite time extinction occurs for non-negative solutions.

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