Exact boundary controllability of the nonlinear Schrödinger equation
The paper deals with the problem of exact boundary controllability of the semilinear Schrödinger equation posed on a bounded domain \(\Omega\in\mathbb{R}^n\) with either the Dirichlet boundary conditions or the Neumann boundary conditions. The authors establish interrelation between dimension \(n\) and smoothness of the Sobolev state space \(H^S(\Omega)\) providing a local exact controllability around any smooth solution of the cubic Schrödinger equation. The semigroup representation of the solution of associated linearized system plays a considerable role in the substantiation of results.
scientific article; zbMATH DE number 5555293
scientific article