Methods and Applications of Analysis

Volume 15 (2008)

Number 2

The Large-time Behavior of Solutions of Hamilton-Jacobi Equations on the Real Line

Pages: 223 – 242

DOI: http://dx.doi.org/10.4310/MAA.2008.v15.n2.a8

Authors

Naoyuki Ichihara

Hitoshi Ishii

Abstract

We investigate the large-time behavior of solutions of the Cauchy problem for Hamilton-Jacobi equations on the real line $R$. We establish a result on convergence of the solutions to asymptotic solutions as time $t$ goes to infinity.

Keywords

Large-time behavior; Hamilton-Jacobi equations; asymptotic solutions

2010 Mathematics Subject Classification

35B40, 49L25, 70H20

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