On the blowup of solutions of a Schrödinger equation with an inhomogeneous damping coefficient

Abstract

We consider the Cauchy problem for the nonlinear self-focusing Schrödinger equation in ℝNwith an inhomogeneous smooth damping coefficient and we prove, for suitable initial data, and in the spirit of the seminal work of R. Glassey, a blowup result for the corresponding local solutions. We also give some lower bound estimates for the blowing-up solutions.