On the stability of the Kawahara equation with a distributed infinite memory

2022/12/05 by Roberto de A. Capistrano–Filho, Boumediène Chentouf, Filho, Roberto de A. Capistrano +3
Engineering · Mathematics · Physics and Astronomy · #93D15 Secondary: 34K25 #93D20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Primary: 35Q53 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.02427

openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article will deal with the stabilization problem for the higher-order dispersive system, commonly called the Kawahara equation. To do so, we introduce a damping mechanism via a distributed memory term in the equation to prove that the solutions of the Kawahara equation are exponentially stable, provided that specific assumptions on the memory kernel are fulfilled. This is possible thanks to the energy method that permits to provide a decay estimate of the system energy.

Related

• Asymptotic behavior of Kawahara equation with memory effect
• Dispersive Decay Bound of Small Data Solutions to Kawahara Equation in a Finite Time Scale
• Stabilization of the Kawahara-Kadomtsev-Petviashvili equation with time-delayed feedback
• Stability of Periodic Travelling Wave Solutions to the Kawahara Equation
• High-Frequency Instabilities of the Kawahara Equation: A Perturbative\n Approach