Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space

Hitoshi Ishii

doi:10.1016/j.anihpc.2006.09.002

Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space

Hitoshi Ishii^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

57 Citations (Scopus)

Abstract

We study the large time behavior of solutions of the Cauchy problem for the Hamilton-Jacobi equation u_t + H (x, D u) = 0 in Rⁿ × (0, ∞), where H (x, p) is continuous on Rⁿ × Rⁿ and convex in p. We establish a general convergence result for viscosity solutions u (x, t) of the Cauchy problem as t → ∞.

Original language	English
Pages (from-to)	231-266
Number of pages	36
Journal	Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
Volume	25
Issue number	2
DOIs	https://doi.org/10.1016/j.anihpc.2006.09.002
Publication status	Published - 2008 Mar

Keywords

Asymptotic solutions
Hamilton-Jacobi equations
Large time behavior
Weak KAM theory

ASJC Scopus subject areas

Analysis

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10.1016/j.anihpc.2006.09.002

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abstract = "We study the large time behavior of solutions of the Cauchy problem for the Hamilton-Jacobi equation ut + H (x, D u) = 0 in Rn × (0, ∞), where H (x, p) is continuous on Rn × Rn and convex in p. We establish a general convergence result for viscosity solutions u (x, t) of the Cauchy problem as t → ∞.",

keywords = "Asymptotic solutions, Hamilton-Jacobi equations, Large time behavior, Weak KAM theory",

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year = "2008",

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AB - We study the large time behavior of solutions of the Cauchy problem for the Hamilton-Jacobi equation ut + H (x, D u) = 0 in Rn × (0, ∞), where H (x, p) is continuous on Rn × Rn and convex in p. We establish a general convergence result for viscosity solutions u (x, t) of the Cauchy problem as t → ∞.

KW - Asymptotic solutions

KW - Hamilton-Jacobi equations

KW - Large time behavior

KW - Weak KAM theory

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ER -

Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space

Abstract

Keywords

ASJC Scopus subject areas

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