@Article{JPDE-14-61, author = {Charles Bu , Randy Shull , Hefei Wang and Millie Chu }, title = {Well-posedness, Decay Estimates and Blow-up Theorem for the Forced NLS}, journal = {Journal of Partial Differential Equations}, year = {2001}, volume = {14}, number = {1}, pages = {61--70}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5469.html} }