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Citation - WoS: 13
Citation - Scopus: 14
Nonlinear Schrödinger Equations on the Half-Line With Nonlinear Boundary Conditions
(Texas State University - San Marcos, 2016) Batal, Ahmet; Özsarı, Türker
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.

Mathematics / Matematik