Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation

被引：0
|
作者：
V. Zh. Sakbaev
机构：
[1] Moscow Institute of Physics and Technology (State University),
来源：
Proceedings of the Steklov Institute of Mathematics | 2013年 / 283卷
关键词：
Cauchy Problem; STEKLOV Institute; Global Existence; Sobolev Inequality; Limit Problem;
D O I：
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中图分类号：
学科分类号：
摘要：
A class of nonlinear Schrödinger operators with singular coefficients is studied. For this class, necessary and sufficient conditions are established for the existence of initial data such that the corresponding solution to the Cauchy problem blows up in finite time. A regularization procedure for the Cauchy problem is proposed, and the limit behavior of the sequence of solutions to the regularized problems is analyzed.
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页码：165 / 180
页数：15
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