Asymptotic Solutions of Hamilton–Jacobi Equations with Semi-Periodic Hamiltonians

摘要

We study the long time behavior of viscosity solutions of the Cauchy problem for Hamilton–Jacobi equations in n. We prove that if the Hamiltonian Hx p is coercive and strictly convex in a mild sense in p and upper semi-periodic in x, then any solution of the Cauchy problem “converges” to an asymptotic solution for any lower semi-almost periodic initial function.