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