Remarks on the vanishing viscosity process of state-constraint Hamilton-Jacobi equations

2021/07/21 by Yuxi Han, Han, Yuxi, Son N. T. Tu +1 · 5 citations
Economics, Econometrics and Finance · Mathematics · #35B40 #35D40 #49J20 #49L25 #70H20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Biology Tumor Growth #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2107.09860

openalex publication_date 2021/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the convergence rate in the vanishing viscosity process of the solutions to the subquadratic state-constraint Hamilton-Jacobi equations. We give two different proofs of the fact that, for nonnegative Lipschitz data that vanish on the boundary, the rate of convergence is O(√(ε)) in the interior. Moreover, the one-sided rate can be improved to O(ε) for nonnegative compactly supported data and O(ε^{1/(p-(1)/(2))}) (where 1

Cited by

• State-Constrained Chemical Reactions: Discrete-to-Continuous Hamilton--Jacobi Equations and Large Deviations
• On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount
• Rate of convergence of the vanishing viscosity method for Hamilton-Jacobi equations with Neumann boundary conditions
• On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints
• Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations

Related

• On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints
• Convergence rates for the vanishing viscosity approximation of Hamilton-Jacobi equations: the convex case
• Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations
• Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations
• Rate of convergence of the vanishing viscosity method for Hamilton-Jacobi equations with Neumann boundary conditions