FINITE-TIME CONVERGENCE OF SOLUTIONS OF HAMILTON-JACOBI EQUATIONS

This paper deals with the long-time behavior of viscosity solutions of evolutionary contact Hamilton-Jacobi equations w(t) + H(x, w, w(x)) = 0, where H(x, u, p) is strictly decreasing in u and satisfies Tonelli conditions in p. We show that each viscosity solution of the ergodic contact Hamilton-Jacobi equation H(x, u, u(x)) = 0 can be reached by many different viscosity solutions of the above evolutionary equation in a finite time.

Automated summary

This paper deals with the long-time behavior of viscosity solutions of evolutionary contact Hamilton-Jacobi equations. It shows the connection between viscosity solutions of the ergodic contact Hamilton-Jacobi equation and solutions of the evolutionary equation.