A forced fractional Schrödinger equation with a Neumann boundary condition. (22nd June 2016)

• Record Type: Journal Article
• Authors: Esquivel, L; Kaikina, Elena I
• Is Part Of: Nonlinearity. Volume 29:Number 7(2016:Jul.)
• Page Start: 2082
• Page End: 2111
• Publication Date: 2016-06-22
• Subjects: asymptotics of solutions -- cubic nonlinear fractional Schrödinger equation -- initial-boundary value problem; 35Q55 -- 35B40; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/7/2082
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study the initial-boundary value problem for the nonlinear fractional Schrödinger equation { u t + i ( u x x + 1 2 π ∫ 0 ∞ s i g n ( x − y ) | x − y | 1 2 u y ( y ) d y ) + i | u | 2 u = 0, t > 0, x > 0 ; u ( x, 0 ) = u 0 ( x ), x > 0, u x ( 0, t ) = h ( t ), t > 0. We prove the global-in-time existence of solutions for a nonlinear fractional Schrödinger equation with inhomogeneous Neumann boundary conditions. We are also interested in the study of the asymptotic behaviour of the solutions.