标题:
一类四阶非线性Schro¨dinger方程的爆破准则Blow-Up Criteria for a Kind of Fourth Order Nonlinear Schro¨dinger Equations
作者:
米彩莲, 卢美虹, 杨晗
关键字:
非线性Schro¨dinger方程, 初值问题, B-G型不等式, 整体解, 爆破准则Nonlinear Schro¨dinger Equation, Initial Value Problem, B-G Type Inequality, Global Solution, Blow-Up Criteria
期刊名称:
《Advances in Applied Mathematics》, Vol.5 No.4, 2016-11-24
摘要:
本文通过改进的B-G型不等式研究了一类四阶非线性Schro¨dinger方程的初边值问题。首先借助半群理论得到初值问题局部解的存在唯一性，其次利用B-G型不等式得到了初值问题经典解整体存在的一个新判定准则，即整体解是否存在可由其H2范数是否爆破决定。
The initial-boundary value problem for a kind of fourth order nonlinear Schro¨dinger equations is studied in this paper. Firstly, with the help of the semi-group theory, the existence and uniqueness of local solution of initial value problem is obtained. Secondly, a new global existence criterion for the classical solution is given by using B-G inequality, namely, that whether the solution globally exists is determined by whether its H2 norm blows up.