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arXiv · 2310.13903

Time periodic and almost periodic viscosity solutions of contact Hamilton-Jacobi equations on $\mathbb{T}^n$

Kaizhi Wang·Jun Yan·Kai Zhao
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Abstract

This paper concerns with the time periodic viscosity solution problem for a class of evolutionary contact Hamilton-Jacobi equations with time independent Hamiltonians on the torus $\mathbb{T}^n$. Under certain suitable assumptions we show that the equation has a non-trivial $T$-periodic viscosity solution if and only if $T\in D$, where $D$ is a dense subset of $[0,+\infty)$. Moreover, we clarify the structure of $D$. As a consequence, we also study the existence of Bohr almost periodic viscosity solutions.

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Kaizhi Wang, Jun Yan, Kai Zhao. 2023-10-21. Time periodic and almost periodic viscosity solutions of contact Hamilton-Jacobi equations on $\mathbb{T}^n$. https://arxiv.org/abs/2310.13903

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