Blow-up rate, mass concentration and asymptotic profile of blow-up solutions for the nonlinear inhomogeneous Schrödinger equation

In this paper, we study the dynamics of blow-up solutions for the nonlinear inhomogeneous Schrödinger equation. Firstly, we show the lower blow-up rate of blow-up solutions by rescaling technique, and use it to get the rate of mass concentration of blow-up solutions. Secondly, for the minimal mass blow-up solutions, we obtain the sharp lower blow-up rate by the variational methods. Finally, we investigate the limiting profile of minimal mass blow-up solutions.