Nonhomogeneous Boundary Value Problems of Nonlinear Schrödinger Equations in a Half Plane
Nonhomogeneous Boundary Value Problems of Nonlinear Schrödinger Equations in a Half Plane
This paper studies the initial-boundary-value problems (IBVPs) of nonlinear Schrödinger equations posed in a half plane $\mathbb{R}\times \mathbb{R}^+$ with nonhomogeneous Dirichlet boundary conditions. For any given $s \ge 0$, if the initial data $\varphi (x, y)$ are in Sobolev space $H^s(\mathbb{R}\times \mathbb{R}^+) $ with the boundary data $ h ( …