Massera's theorems for a higher order dispersive system

TL;DR

This paper extends Massera's theorems to the Kawahara system, a higher order dispersive PDE, demonstrating conditions under which solutions are periodic, quasi-periodic, or almost periodic based on semigroup properties and decay estimates.

Contribution

It introduces Massera-type theorems for the Kawahara system, establishing periodicity and related properties for solutions in a bounded domain.

Findings

Solutions exhibit periodic, quasi-periodic, and almost periodic behavior.

Semigroup properties and decay rates are key to proving solution behaviors.

The results apply to higher order dispersive equations in bounded domains.

Abstract

This work is devoted to present Massera-type theorems for the Kawahara system, a higher order dispersive equation, posed in a bounded domain. Precisely, thanks to some properties of the semigroup and the decays of the solutions of this equation, we are able to prove its solutions are periodic, quasi-periodic and almost periodic.