Nonlinear boundary feedback stabilization for Schrödinger equations (Q1906541)

The purpose of this paper is to discuss the following problem: \[ \begin{aligned} iy_t+ \Delta y & = 0,\quad \text{in}\quad \Omega\times (0, +\infty)\\ {\partial y\over \partial\nu}+ g(y_t) & = 0,\quad \text{on}\quad \Gamma_0\times (0, +\infty)\end{aligned} \] \[ y= 0,\quad \text{on}\quad \Gamma_1\times (0, +\infty),\quad y(0)= y_0,\quad \text{in}\quad \Omega, \] where \(\Omega\subset \mathbb{R}^N\) is a bounded domain with boundary \(\partial\Omega= \Gamma_0\cup \Gamma_1\). The authors study the existence, uniqueness and the asymptotic behavior of the solutions by using nonlinear semigroup theory.