Abstract
Consider the nonlinear Schrödinger equationu t −iΔu=f(u). Forf(u)=±|u|1+p , ±i|u|1+p , ±u|u| p (p>0), and the Dirichlet boundary or nonlinear boundary (including the Neumann boundary and the Robin boundary) conditions, we establish the local estimates for the timet to the solutions of the initial-boundary value problems. Being based up on these estimates, we investigate the blowing-up properties of the solutions.
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