A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations

2012/10/26 by Guy Barles, Barles, Guy, Hitoshi Ishii +3
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Variational Analysis #Quantum chaos and dynamical systems #Stochastic processes and financial applications #math.AP

paper · pdf · doi:10.48550/arxiv.1210.7220

arxiv created 2012/10/26 · openalex publication_date 2012/10/26 · arxiv updated 2012/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new PDE approach to establishing the large time asymptotic behavior of solutions of Hamilton-Jacobi equations, which modifies and simplifies the previous ones (Barles and Souganidis, 2000; Barles, Ishii and Mitake, 2012), under a refined "strict convexity" assumption on the Hamiltonians. Not only such "strict convexity" conditions generalize the corresponding requirements on the Hamiltonians in Barles and Souganidis (2000), but also one of the most refined our conditions covers the situation studied in Namah and Roquejoffre (1999).

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