Well-posedness, Decay Estimates and Blow-up Theorem for the Forced NLS (Journal of Partial Differential Equations, 2001)
In this article we prove that the following NLS iu_t = u_{zz}-g|u|^{P-1}u,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.
Keywords: Nonlinear Schrödinger equation; well-posedness; decay estimates; blow-up