On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916960186400768 |
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| author | Wang, Zibo Zhang, Jianlu |
| author_facet | Wang, Zibo Zhang, Jianlu |
| contents | In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): \[
λu +H(x, du)=\varepsilon(λ)Δu,\quad λ>0 \]
as $λ\rightarrow 0_+$, once the modulus $\varepsilon(λ)$ satisfies $\varlimsup_{λ\rightarrow 0_+}\varepsilon(λ)/λ=0$. Such an exponent of $\varepsilon(λ)$ is nearly optimal in the convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount Wang, Zibo Zhang, Jianlu Analysis of PDEs Dynamical Systems Optimization and Control In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): \[ λu +H(x, du)=\varepsilon(λ)Δu,\quad λ>0 \] as $λ\rightarrow 0_+$, once the modulus $\varepsilon(λ)$ satisfies $\varlimsup_{λ\rightarrow 0_+}\varepsilon(λ)/λ=0$. Such an exponent of $\varepsilon(λ)$ is nearly optimal in the convergence. |
| title | On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount |
| topic | Analysis of PDEs Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2509.17402 |