Abstract
We study some properties of the remotely almost periodic functions. This paper studies viscosity solutions of general Hamilton-Jacobi equations in the time remotely almost periodic case. Existence and uniqueness results are presented under usual hypotheses.
Highlights
In this paper we consider the viscosity solutions of first-order Hamilton-Jacobi equations of the form∂tu H x, u, Du f t, x, t ∈ ÊN × Ê.This problem was studied in 1 in the time periodic and almost periodic cases
This paper studies viscosity solutions of general Hamilton-Jacobi equations in the time remotely almost periodic case
In this paper we study this problem in a more regular condition, that is, in the time remotely almost periodic case
Summary
∂tu H x, u, Du f t , x, t ∈ ÊN × Ê This problem was studied in 1 in the time periodic and almost periodic cases. In this paper we study this problem in a more regular condition, that is, in the time remotely almost periodic case. We will look for such viscosity solutions when the Hamiltonian H and f are continuous functions f is remotely almost periodic in t. For the definition of viscosity subsolution and supersolution the reader can refer to 11
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