On the decay of viscosity solutions to Hamilton–Jacobi equations with almost periodic initial data

Abstract

The Cauchy problem is treated for a multidimensional Hamilton–Jacobi equation with a merely continuous nonstrictly convex Hamiltonian and a Bohr almost periodic initial function. Under the condition that the Hamiltonian is not degenerate in resonant directions (laying in the additive group generated by the spectrum of the initial function), the uniform decay of the viscosity solution to the constant equal to the infimum of the initial function is established.