Boundary Exponential Stabilization for the Linear KP-II equation without Critical Size Restrictions

Abstract: 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 $\Omega = (0, L) \times (0, L)$, $ L > 0 $. Furthermore, we examine the interaction between the drift term $u_x$ under these constraints.