On the Large Time Behavior of Solutions of Hamilton--Jacobi Equations
Guy Barles, Panagiotis E. Souganidis · SIAM Journal on Mathematical Analysis · 2000
We consider the long time behavior of viscosity solutions of first-order Hamilton--Jacobi equations with periodic space dependence. We prove, under sharp conditions, that as time goes to infinity, solutions converge to solutions of the corresponding stationary equation.