On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount

2025/09/22 by Wang, Zibo, Zhang, Jianlu
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2509.17402

Abstract

In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): λu +H(x, du)=ε(λ)Δu, λgt;0 as λ→ 0₊, once the modulus ε(λ) satisfies \varlimsup_{λ→ 0+}ε(λ)/λ=0. Such an exponent of ε(λ) is nearly optimal in the convergence.

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Related

• On the negative limit of viscosity solutions for discounted Hamilton-Jacobi equations
• Remarks on the rate of convergence of the vanishing viscosity process of Hamilton-Jacobi equations
• Finite-time convergence of solutions of Hamilton-Jacobi equations
• Convergence rates for the vanishing viscosity approximation of Hamilton-Jacobi equations: the convex case
• Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations