Abstract
We study the initial-boundary value problem for the nonlinear fractional Schrödinger equation0,~x>0; \\\\ u(x,0)={{u}_{0}}(x),~x>0,{{u}_{x}}(0,t)=h(t),~t>0. \\end{array}\\right. \\end{eqnarray} ?>{ut+i(uxx+12π∫0∞sign(x−y)|x−y|12uy( y)dy)+i|u|2u=0, t>0, x>0;u(x,0)=u0(x), x>0,ux(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.
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