Logarithmic Stabilization of the Schrödinger Equation With Dynamic Boundary Condition

ABSTRACT This paper addresses the stabilization problem for the Schrödinger equation with dynamic boundary condition of Wentzell type. Under suitable assumption about the damping domain, we demonstrate that sufficiently smooth solutions of the Schrödinger equation decay logarithmically. The proof is based on some frequency estimates with exponential loss on the resolvent operators, which will be solved by establishing an interpolation inequality for a suitable parabolic equation with Wentzell‐type boundary condition.