Global Stabilization for the BBM-KP equations on R2

2024/10/02 by Gallego, F. A., Martinez, V. H. Gonzalez, Grajales, J. C. Muñoz
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2410.01998

Abstract

In this paper, we present results on the energy decay of the BBM-KP equations (I and II) posed on \R² 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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