论文标题
半平面上非线性Schrödinger方程的Robin和Neumann问题
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane
论文作者
论文摘要
这项工作研究了半平面上二维非线性Schrödinger方程的初始值问题，并在Sobolev空间中使用初始数据，以及适当的波尔加因空间中的Neumann或Robin边界数据。它通过利用通过FOKAS的统一变换获得的强制线性初始界价值问题和收缩映射参数来建立Hadamard的良好性。
This work studies the initial-boundary value problem of the two-dimensional nonlinear Schrödinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It establishes well-posedness in the sense of Hadamard by utilizing the explicit solution formula for the forced linear initial-boundary value problem obtained via Fokas's unified transform, and a contraction mapping argument.
