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Title: Nonlinear schrödinger equations on the half-line with nonlinear boundary conditions
Authors: Batal, Ahmet
Özsarı, Türker
Batal, Ahmet
Özsarı, Türker
Keywords: Nonlinear Schrödinger equation
Nonlinear boundary conditions
Inhomogeneous boundary conditions
Local well-posedness
Issue Date: Aug-2016
Publisher: Texas State University - San Marcos
Source: Batal, A., and Özsarı, T. (2016). Nonlinear schrödinger equations on the half-line with nonlinear boundary conditions. Electronic Journal of Differential Equations, 2016, 1-20.
Abstract: In this article, we study the initial boundary value problem for nonlinear Schrödinger equations on the half-line with nonlinear boundary conditions ux(0, t) + λ|u(0, t)|ru(0, t) = 0, λ ∈ ℝ − {0}, r > 0. We discuss the local well-posedness when the initial data u0 = u(x, 0) belongs to an L2-based inhomogeneous Sobolev space (formula presented) with (formula presented). We deal with the nonlinear boundary condition by first studying the linear Schrödinger equation with a time-dependent inhomogeneous Neumann boundary condition ux(0, t) = h(t) where (formula presented) (0, T). © 2016 Texas State University.
ISSN: 1072-6691
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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