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January/February 2009 Sharp decay estimates and vanishing viscosity for diffusive Hamilton-Jacobi equations
Matania Ben-Artzi, Saïd Benachour, Philippe Laurençot
Adv. Differential Equations 14(1/2): 1-25 (January/February 2009).

Abstract

Sharp temporal decay estimates are established for the gradient and time derivative of solutions to the Hamilton-Jacobi equation $\partial_t {v_\varepsilon} + H(|\nabla_x {v_\varepsilon} |)= \varepsilon \Delta {v_\varepsilon}$ in ${\mathbb{R}^N\times(0,\infty)}$, the parameter $\varepsilon$ being either positive or zero. Special care is given to the dependence of the estimates on $\varepsilon$. As a by-product, we obtain convergence of the sequence $({v_\varepsilon})$ as $\varepsilon\to 0$ to a viscosity solution, the initial condition being only continuous and either bounded or nonnegative. The main requirement on $H$ is that it grows superlinearly or sublinearly at infinity, including in particular $H(r)=r^p$ for $r\in [0,\infty)$ and $p\in (0,\infty)$, $p\ne 1$.

Citation

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Matania Ben-Artzi. Saïd Benachour. Philippe Laurençot. "Sharp decay estimates and vanishing viscosity for diffusive Hamilton-Jacobi equations." Adv. Differential Equations 14 (1/2) 1 - 25, January/February 2009.

Information

Published: January/February 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1175.35031
MathSciNet: MR2478927

Subjects:
Primary: 35F25, 35K15, 35K55, 49L25

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.14 • No. 1/2 • January/February 2009
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