Blow-up of solutions of Cauchy problem for nonlinear Schrödinger equation

Abstract

In this work we study the effect of time finiteness of the existence of Cauchy problem for nonlinear Schrödinger equation solution. Together with the ill-posed Cauchy problem we consider its neighborhood in the space of operators, representing Cauchy problem. We explore the convergence of sequence of solutions of Cauchy problems with the operators, approximating the initial Hamiltonian.

Keywords

• nonlinear schrödinger equation
• regularization
• blow-up regime
• blow-up of solution
• viscosity solution