State-constraint static Hamilton-Jacobi equations in nested domains

Yeoneung Kim; Hung V. Tran; Son N. Tu

doi:10.1137/19M1292035

State-constraint static Hamilton-Jacobi equations in nested domains

Yeoneung Kim, Hung V. Tran, Son N. Tu

Dept. of Applied Artificial Intelligence

University of Wisconsin-Madison

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

9 Scopus citations

Abstract

We study state-constraint static Hamilton-Jacobi equations in a sequence of domains {Ω_k\}_kϵNin Rⁿsuch that Ω_k⊂Omega;_k+1k ϵ N We obtain rates of convergence of u_k, the solution to the state-constraint problem in Ω_k, to u, the solution to the corresponding problem in Ω = ∪_kϵNΩ_k. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.

Original language	English
Pages (from-to)	4161-4184
Number of pages	24
Journal	SIAM Journal on Mathematical Analysis
Volume	52
Issue number	5
DOIs	https://doi.org/10.1137/19M1292035
State	Published - 2020

Keywords

First-order Hamilton-Jacobi equations
Optimal control theory
Rate of convergence
State-constraint problems
Viscosity solutions

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10.1137/19M1292035

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abstract = "We study state-constraint static Hamilton-Jacobi equations in a sequence of domains {Ωk\}kϵNin Rnsuch that Ωk⊂Omega;k+1k ϵ N We obtain rates of convergence of uk, the solution to the state-constraint problem in Ωk, to u, the solution to the corresponding problem in Ω = ∪kϵNΩk. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.",

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AU - Tran, Hung V.

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AB - We study state-constraint static Hamilton-Jacobi equations in a sequence of domains {Ωk\}kϵNin Rnsuch that Ωk⊂Omega;k+1k ϵ N We obtain rates of convergence of uk, the solution to the state-constraint problem in Ωk, to u, the solution to the corresponding problem in Ω = ∪kϵNΩk. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.

KW - First-order Hamilton-Jacobi equations

KW - Optimal control theory

KW - Rate of convergence

KW - State-constraint problems

KW - Viscosity solutions

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 5

ER -

State-constraint static Hamilton-Jacobi equations in nested domains

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