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arXiv · 2305.18586

Asymptotic behavior of Kawahara equation with memory effect

Roberto de A. Capistrano Filho·Boumediène Chentouf·Isadora Maria de Jesus
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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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Roberto de A. Capistrano Filho, Boumediène Chentouf, Isadora Maria de Jesus. 2023-05-29. Asymptotic behavior of Kawahara equation with memory effect. https://arxiv.org/abs/2305.18586

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