Asymptotic behavior of Kawahara equation with memory effect

2023/05/29 by Roberto de A. Capistrano–Filho, Boumediène Chentouf, Filho, Roberto de A. Capistrano +3
Mathematics · Physics and Astronomy · #37L50 #93D15 #93D30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2305.18586

openalex publication_date 2023/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we are interested in a detailed qualitative analysis of the Kawahara equation, a model that has numerous physical motivations such as magneto-acoustic waves in a cold plasma and gravity waves on the surface of a heavy liquid. First, we design a feedback control law, which combines a damping component and another one of finite memory-type. Then, we are capable of proving that the problem is well-posed under a condition involving the feedback gains of the boundary control and the memory kernel. Afterwards, it is shown that the energy associated with this system exponentially decays.

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