Type: Article

A forced fractional Schrödinger equation with a Neumann boundary condition

Esquivel L.; Kaikina, E.;

Abstract:

We study the initial-boundary value problem for the nonlinear fractional Schrodinger equation {u(t) + i(u(xx) + 1/2 pi integral(infinity)(0) sign(x - y)/vertical bar x - y vertical bar(1/2)u(y)(y)dy) + i vertical bar u vertical bar(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 Schrodinger equation with inhomogeneous Neumann boundary conditions. We are also interested in the study of the asymptotic behaviour of the solutions.