In this paper, we delve into the intricacies of boundary stabilization for the linearized KP-II equation within the constraints of a bounded domain, a phenomenon known as ``critical length." Our primary aim is to design a feedback law that ensures the existence and exponential stabilization of solutions in the energy space, without length restrictions on the domain Ω=(0,L)×(0,L), L>0. Furthermore, we examine the interaction between the drift term ux under these constraints.
@article{arxiv.2312.02294,
title = {Boundary Exponential Stabilization for the Linear KP-II equation without Critical Size Restrictions},
author = {F. A. Gallego and J. R. Muñoz},
journal= {arXiv preprint arXiv:2312.02294},
year = {2025}
}