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arXiv · 2410.01998

Global Stabilization for the BBM-KP equations on R2

F. A. Gallego·V. H. Gonzalez Martinez·J. C. Muñoz Grajales
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Abstract

In this paper, we present results on the energy decay of the BBM-KP equations (I and II) posed on $\R^2$ with localized damping. This model offers an alternative to the KP equations, analogous to how the regularized long-wave equation relates to the classical Korteweg-de Vries (KdV) equation. We show that the energy associated with the Cauchy problem decays exponentially when a localized dissipative mechanism is present in a subdomain. Finally, we validate the theoretical results on the exponential stabilization of solutions to the BBM-KP equations with damping through numerical experiments using a spectral-finite difference scheme.

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F. A. Gallego, V. H. Gonzalez Martinez, J. C. Muñoz Grajales. 2024-10-02. Global Stabilization for the BBM-KP equations on R2. https://arxiv.org/abs/2410.01998

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