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

Said Benachour·Simona Dabuleanu-Hapca·Philippe Laurençot
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Abstract

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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Said Benachour, Simona Dabuleanu-Hapca, Philippe Laurençot. 2006-09-12. Decay Estimates for a Viscous Hamilton-Jacobi Equation with Homogenious Dirichet Boundary Conditions. https://arxiv.org/abs/math/0609332

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