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三维空间中带磁场项的非线性Schrdinger方程的爆破解 被引量：1

The Blow-up Solution of the Nonlinear Schrdinger Equation with Magnetic Field in Three Dimension
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摘要 研究三维空间中带磁场项的非线性Schrdinger方程,也称为带奇异积分算子的非线性Schrdinger方程的柯西问题.通过构造强制变分问题,克服了非线性奇异积分算子所带来的困难,得到当初值和初始能量满足一定条件时,所研究方程柯西问题的解在有限时间内爆破. In this paper, we study the Cauchy problem of the nonlinear Sehrodinger equations with magnetic field in three space dimensions. By constructing the constrained variational problem, we obtain the solution to the Cauehy problem for the equations blows up in finite time when initial data and initial energy satisfy certain conditions.
作者 帅鲲 蒲志林
机构地区 四川师范大学成都学院 四川师范大学数学与软件科学学院
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第6期719-725,共7页 Journal of Sichuan Normal University（Natural Science）
基金 国家自然科学基金(11171241)资助项目
关键词 非线性Schrdinger方程 爆破 磁场 柯西问题 强制变分问题 nonlinear Schr＇odinger equation blow-up magnetic field Cauehy problem the constrained variational problem
分类号 O175.26 [理学—基础数学]
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参考文献15

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二级参考文献46

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共引文献4

同被引文献12

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  • 6Yang Z J. Global attrator for the Kirchhoff type equation with a strong dissipation [J]. Diff Eqns,2010,249(3):3258-3278.
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  • 8Filippov D O, Vittorino P. Long-term analysis of strongly damped nonlinear wave equations[J].Nonlinearity,2011(24):3413-3435.
  • 9张媛媛.一类非线性发展方程的整体吸引子[J].吉林师范大学学报（自然科学版）,2012,33(2):21-28. 被引量：3
  • 10李金蔚,蒲志林,邓伟.强阻尼波动方程组解的性质[J].四川师范大学学报（自然科学版）,2013,36(5):649-654. 被引量：1

引证文献1

四川师范大学学报（自然科学版）
2012年 第6期

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