(untitled) (Journal of Partial Differential Equations, 2001)
In this article we prove that the following NLS iu_t = u_zz-g|u|^P-1u,g > O, x, t > 0 with either Dirichlet or Robin boundary condition at x = 0 is well-posed. L^p + 1 decay estimates, blow-up theorem and numerical results are also given.