Geodesic
On almost periodic viscosity solutions to Hamilton-Jacobi equations
Minimax theory and its applications, Tome 5 (2020) no. 2
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We establish that a viscosity solution to a multidimensional Hamilton-Jacobi 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 non-degenerate hamiltonian we prove the decay property of almost periodic viscosity solutions when time t → +∞. For convex hamiltonian we also provide another proof of this property using the Hopf-Lax-Oleinik formula. For periodic solutions the more general result is proved on unconditional asymptotic convergence of a viscosity solution to a traveling wave.
Mots-clés : Hamilton-Jacobi equations, viscosity solutions, almost periodic functions, long time behavior 
@article{MTA_2020_5_2_a12,
     author = {Evgeny Yu. Panov},
     title = {On almost periodic viscosity solutions to {Hamilton-Jacobi} equations},
     journal = {Minimax theory and its applications},
     year = {2020},
     volume = {5},
     number = {2},
     zbl = {1452.35067},
     url = {http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a12/}
}
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Evgeny Yu. Panov. On almost periodic viscosity solutions to Hamilton-Jacobi equations. Minimax theory and its applications, Tome 5 (2020) no. 2. http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a12/