The Robin and Neumann problems for the nonlinear Schrodinger equation on the half-plane

被引：1

作者：

Himonas, A. Alexandrou ^{[1
]}

Mantzavinos, Dionyssios ^{[2
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2022年 / 478卷 / 2265期

基金：

美国国家科学基金会;

关键词：

two-dimensional nonlinear Schrodinger equation; initial-boundary value problem with Neumann and Robin boundary conditions; unified transform method of Fokas; well-posedness in Sobolev spaces; Bourgain spaces; linear space-time estimates; BOUNDARY-VALUE-PROBLEM; DE-VRIES EQUATION; TRANSFORM METHOD; WAVES; MODULATION; REGULARITY;

D O I：

10.1098/rspa.2022.0279

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This work studies the initial-boundary value problem (ibvp) of the two-dimensional nonlinear Schrodinger 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 using the explicit solution formula for the forced linear ibvp obtained via Fokas's unified transform, and a contraction mapping argument.

引用

页数：20

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