Homogenization of monotone systems of Hamilton-Jacobi equations

TL;DR

This paper investigates the homogenization process for monotone systems of periodic Hamilton-Jacobi equations, establishing the limit behavior and convergence of solutions to a homogenized system via cell problems.

Contribution

It characterizes the effective Hamiltonians for the limit problem and proves uniform convergence of solutions in monotone systems of Hamilton-Jacobi equations.

Findings

Characterization of limit Hamiltonians through cell problems

Proof of uniform convergence of solutions

Establishment of homogenized system for monotone Hamilton-Jacobi systems

Abstract

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the uniform convergence of the solution of the oscillating systems to the bounded uniformly continuous solution of the homogenized system.