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 \begin{equation*} w_t+H(x,w,w_x)=0, \end{equation*} 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. [ABSTRACT FROM AUTHOR]