
Minimax Theory and its Applications 05 (2020), No. 2, 383400 Copyright Heldermann Verlag 2020 On Almost Periodic Viscosity Solutions to HamiltonJacobi Equations Evgeny Yu. Panov Algebra and Analysis Department, Novgorod State University, Veliky Novgorod 173003, Russia; and: Peoples’ Friendship University, Moscow 117198, Russia eugeny.panov@novsu.ru We establish that a viscosity solution to a multidimensional HamiltonJacobi equation with Bohr almost periodic initial data remains to be spatially almost periodic and the additive subgroup generated by its spectrum does not increase in time. In the case of one space variable and a nondegenerate hamiltonian we prove the decay property of almost periodic viscosity solutions when time t goes to ∞. For convex hamiltonian we also provide another proof of this property using the HopfLaxOleinik formula. For periodic solutions the more general result is proved on unconditional asymptotic convergence of a viscosity solution to a traveling wave. Keywords: HamiltonJacobi equations, viscosity solutions, almost periodic functions, long time behavior. MSC: 35F21 35D40 35B15; 35B40. [ Fulltextpdf (148 KB)] for subscribers only. 