On Almost Periodic Viscosity Solutions to Hamilton-Jacobi Equations

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 -> +infinity. 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.

Авторы
Panov E.Y. 1, 2
Издательство
HELDERMANN VERLAG
Номер выпуска
2
Язык
Английский
Страницы
383-400
Статус
Опубликовано
Том
5
Год
2020
Организации
  • 1 Novgorod State Univ, Algebra & Anal Dept, Veliky Novgorod 173003, Russia
  • 2 Peoples Friendship Univ, RUDN Univ, Moscow 117198, Russia
Ключевые слова
Hamilton-Jacobi equations; viscosity solutions; almost periodic functions; long time behavior
Дата создания
20.04.2021
Дата изменения
20.04.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/73158/
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