具弱耗散项的非线性Hartree方程

数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 259-265.

具弱耗散项的非线性Hartree方程

黄娟|张健

四川师范大学数学与软件科学学院成都 610066

收稿日期:2012-09-10 修回日期:2013-11-07 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
国家自然科学基金(10771151, 11126335)、四川省教育厅青年基金(10ZB003)和四川省科技厅科研基金(2010JY0057, 2012JQ0041)资助.

The Weakly Damped Nonlinear Hartree Equation

HUANG Juan, ZHANG Jian

College of Mathematics and Software Science, Sichuan Normal University, Chengdu 61006

Received:2012-09-10 Revised:2013-11-07 Online:2014-04-25 Published:2014-04-25
Supported by:
国家自然科学基金(10771151, 11126335)、四川省教育厅青年基金(10ZB003)和四川省科技厅科研基金(2010JY0057, 2012JQ0041)资助.

摘要/Abstract

摘要：

该文讨论了一类在量子理论中有着较多应用的具耗散项的非线性Hartree方程. 分别从耗散系数和初值两个方面讨论了解的整体存在性条件. 一方面, 利用Strichartz估计, 得到仅依赖于耗散系数的整体存在性条件. 另一方面, 也得到了仅依赖于初值大小的整体存在性条件. 而且, 还得到了一个整体解存在的小初值准则.

关键词: Hartree方程, 耗散, 整体存在

Abstract:

This paper is concerned with the weakly damped nonlinear Hartree equation which has many interesting applications in quantum theory. We discuss the global existence of this equation from two aspects, the damped coefficients and the
initial data, respectively. By Strichartz estimate, we obtain a global existence result which depends on the size of the damped parameter. We also get the other global existence result depending on the initial data. Moreover, a small initial data criterion of global existence is obtained.

Key words: Hartree equation, Damped, Global existence

中图分类号:

78A60

黄娟, 张健. 具弱耗散项的非线性Hartree方程[J]. 数学物理学报, 2014, 34(2): 259-265.

HUANG Juan, ZHANG Jian. The Weakly Damped Nonlinear Hartree Equation[J]. Acta mathematica scientia,Series A, 2014, 34(2): 259-265.

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