Ahmet Batal, Turker Ozsari
Abstract:
In this article, we study the initial boundary value problem for
nonlinear Schrodinger equations on the half-line with nonlinear
boundary conditions
We discuss the local well-posedness when the initial data
belongs to an
-based
inhomogeneous Sobolev space
with
.
We deal with the nonlinear boundary condition by first studying the linear
Schrodinger equation with a time-dependent inhomogeneous Neumann boundary
condition
where
.
Submitted March 2, 2016. Published August 17, 2016.
Math Subject Classifications: 35Q55, 35A01, 35A02, 35B30.
Key Words: Nonlinear Schrodinger equations; nonlinear boundary conditions;
local well-posedness; inhomogeneous boundary conditions.
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Ahmet Batal Department of Mathematics Izmir Institute of Technology Izmir, Turkey email: ahmetbatal@iyte.edu.tr | |
Turker Ozsari Department of Mathematics Izmir Institute of Technology Izmir, Turkey email: turkerozsari@iyte.edu.tr |
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