Hung V. Tran

activity

20232026

most citedQuantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications

1 citations · 1 across the 10 of their papers we have counts for

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math.AP2026

Pathological viscosity solutions of Hamilton--Jacobi equations

Hung V. Tran, Yifeng Yu

We construct a continuous function $u$ on the closed unit ball in $R^{4}$ and a smooth autonomous Hamiltonian $H : R^{4} \to [1, 2]$ for which $u$ solves $H (D u) = c$ in the…

math.AP2026

Vanishing discount and viscosity selection problems for mechanical Hamilton--Jacobi equations

Hiroyoshi Mitake, Panrui Ni, Hung V. Tran

We study simultaneous vanishing discount and viscosity limits for mechanical Hamilton--Jacobi equations on the $n$ -dimensional torus. In the critical regime, we explicitly identify…

math.AP2026

$L^{\infty}$ Variational Approximation of the Aubry Set

Hung V. Tran, Yifeng Yu

Let $H \in C^{\infty} (R^{n} \times T^{n})$ be a periodic Tonelli Hamiltonian with critical value $c$ . For each $k \in N$ , let $u_{k}$ be the normalized minimizer of the…

math.AP2026

Optimal convergence rates in periodic homogenization of nonconvex Hamilton--Jacobi equations

Jiwoong Jang, Qi Sun, Hung V. Tran +1

We study the convergence rates in periodic homogenization of general nonconvex, coercive Hamilton--Jacobi equations. We show that the optimal convergence rate is $O(\varepsilon^{1/…

math.AP2026

Turbulent Flame Speed Can Increase under Curvature Smoothing

Hung V. Tran, Jack Xin, Yifeng Yu

Curvature effects are expected to smooth flame-front wrinkles and thereby reduce turbulent flame speed. We construct a smooth three-dimensional periodic shear flow for which introd…

math.AP2026

Sharp global and almost everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations

Ziran Liu, Hung V. Tran, Yifeng Yu

We study the periodic homogenization of the viscous Hamilton--Jacobi equation \[ u_t^\varepsilon + \frac{1}{2}|Du^\varepsilon|^2 + V\!\left(\frac{x}{\varepsilon}\right) = \frac{\va…

math.AP2025

Quantitative homogenization of convex Hamilton-Jacobi equations with $u / ε$ -periodic Hamiltonians

Hiroyoshi Mitake, Panrui Ni, Hung V. Tran

Here, we study quantitative homogenization of first-order convex Hamilton-Jacobi equations with $(u / ε)$ -periodic Hamiltonians which typically appear in dislocation dynami…

math.AP2024

Discrete Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel

Jiwoong Jang, Hung V. Tran

Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete…

math.AP2024★ 1 cited

Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications

Yuxi Han, Wenjia Jing, Hiroyoshi Mitake +1

We study the periodic homogenization problem of state-constraint Hamilton--Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We…

math.AP2024

Quenching for axisymmetric hypersurfaces under forced mean curvature flows

Hiroyoshi Mitake, Yusuke Oka, Hung Vinh Tran

Here, we study the motion of axisymmetric hypersurfaces ${Γ_{t}}_{t \geq 0}$ evolved by forced mean curvature flows in the periodic setting. We establish conditions that quenching occ…

math.AP2023

Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals

Hiroyoshi Mitake, Hung V. Tran

Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appr…

Pathological viscosity solutions of Hamilton--Jacobi equations

Vanishing discount and viscosity selection problems for mechanical Hamilton--Jacobi equations

L∞ Variational Approximation of the Aubry Set

Optimal convergence rates in periodic homogenization of nonconvex Hamilton--Jacobi equations

Turbulent Flame Speed Can Increase under Curvature Smoothing

Sharp global and almost everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations

Quantitative homogenization of convex Hamilton-Jacobi equations with u/ε-periodic Hamiltonians

Discrete Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel

Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications

Quenching for axisymmetric hypersurfaces under forced mean curvature flows

Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals

$L^{\infty}$ Variational Approximation of the Aubry Set

Quantitative homogenization of convex Hamilton-Jacobi equations with $u / ε$ -periodic Hamiltonians