8 papers · 1 filter
Convergence Rate of Birkhoff Average for Toral Quasi-Periodic Rotations and Applications
Son N. T. Tu, Jianlu Zhang, Siyao Zhu
In this paper, we establish quantitative Denjoy--Koksma type estimates for higher-dimensional quasi-periodic torus rotations. For Diophantine frequency vectors, we establish quanti…
Quantitative homogenization for static contact Hamilton-Jacobi equations
Gengyu Liu, Son N. T. Tu, Jianlu Zhang
We characterize possible pairs addressing the homogenization problem for Hamilton…
Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions
Yuxi Han, Son Tu
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation o…
On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints
Prerona Dutta, Khai T. Nguyen, Son N. T. Tu
In this paper, we investigate the convergence rate in the vanishing viscosity limit for solutions to superquadratic Hamilton--Jacobi equations with state constraints. For every $p>…
Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains
Son N. T. Tu, Jianlu Zhang
We study the asymptotic behavior of solutions to the fully nonlinear Hamilton-Jacobi equation in as . Under the assumption that the Au…
Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions
Russell Schwab, Son Tu, Olga Turanova
In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravit…