一类四阶非线性Schrodinger方程的爆破准则.pdfVIP

Advances in Applied Mathematics 应用数学进展, 2016, 5(4), 672-682 Published Online November 2016 in Hans. /journal/aam /10.12677/aam.2016.54079 Blow-Up Criteria for a Kind of Fourth Order Nonlinear Schrödinger Equations Cailian Mi, Meihong Lu, Han Yang College of Mathematics, Southwest Jiaotong University, Chengdu Sichuan rd th th Received: Nov. 3 , 2016; accepted: Nov. 19 , 2016; published: Nov. 24 , 2016 Copyright © 2016 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Open Access Abstract The initial-boundary value problem for a kind of fourth order nonlinear Schrödinger 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. Keywords Nonlinear Schrödinger Equation, Initial Value Problem, B-G Type Inequality, Global Solution, Blow-Up Criteria 一类四阶非线性Schrödinger方程的爆破准则 米彩莲，卢美虹，杨 晗 西南交通大学数学学院，四川 成都 收稿日期：2016年11月3 日；录用日期：2016年11月19 日；发布日期：2016年11月24 日 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Schrödinger方程的初边值问题。首先借助半群理论 文章引用: 米彩莲, 卢美虹, 杨晗. 一类四阶非线性 Schrödinger 方程的爆破准则[J]. 应用数学进展, 2016, 5(4): 672-682. /10.12677/aam.2016.54079 米彩莲 等 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 2 定准则，即整体解是否存在可由其H 范数是否爆破决定。 关键词 非线性Schrödinger方程，