This book gives an extensive survey of many important topics in the theory of Hamilton–
Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly …

Mean field game (MFG) systems describe equilibrium configurations in games with infinitely
many interacting controllers. We are interested in the behavior of this system as the horizon …

We study the optimal rate of convergence in periodic homogenization of the viscous
Hamilton–Jacobi equation in subject to a given initial datum. We prove that for any given …

We study a class of nondivergence form second-order degenerate linear parabolic
equations in (−∞, T)× R+ d with the homogeneous Dirichlet boundary condition on (−∞ …

In this article, we demonstrate a polynomial convergence rate for homogenization of
Hamilton–Jacobi equations with quasi-periodic potentials. We establish a connection …

In this study, the effect of aqueous ions and sediment inhibitors on asphaltene aggregation
was investigated. The effect of NaCl, MgCl 2 and CaCl 2 salts on three asphaltene models of …

Let u ε and u be viscosity solutions of the oscillatory Hamilton–Jacobi equation and its
corresponding effective equation. Given bounded, Lipschitz initial data, we present a simple …

By constructing appropriate smooth, possibly non-convex supersolutions, we establish
sharp lower bounds near the boundary for the modulus of nontrivial solutions to singular and …

We study state-constraint static Hamilton--Jacobi equations in a sequence of domains
{\Omega_k\}_k∈N in R^n such that \Omega_k⊂k+1 for all k∈N. We obtain rates of …

We study the connection between the Aubry-Mather theory and a mean-field game (MFG)
price-formation model. We introduce a framework for Mather measures that is suited for …