林太家臺灣大學：數學研究所許本源Hsu, Pen-YuanPen-YuanHsu2007-11-282018-06-282007-11-282018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/59486此篇論文裡,我們研究的是非線性薛丁格方程組的爆破解,方程組中的非 線性項係數為時間的函數。主要定理說明了此方程組能找到一組解 (Φ,Ψ)使得∥▽Φ∥L2(Ω)和∥▽Ψ∥L2(Ω)同時爆破,但我們並不清楚∥Φ∥L∞(Ω)和∥Ψ∥L∞(Ω)是否會同時爆破。Here we study finite-time blow-up solutions of two-component system of nonlinear Schr¨odinger equations with a time-dependent nonlinearity. From main theorem in this paper, the system may have a solution (Φ,Ψ) such that both ∥▽Φ∥L2(Ω) and ∥▽Ψ∥L2(Ω) blow up at the same time but we don’t know whether ∥Φ∥L∞(Ω) and ∥Ψ∥L∞(Ω) blow up simultaneously.Contents Abstract(in Chinese) i Abstract(in English) ii Contents iii 1.Introduction 1 2.Preliminary 4 3.Proof of Theorem 1.1 11 References 14531407 bytesapplication/pdfen-US非線性薛丁格爆破解Nonlinear Schrodinger EquationBlow up solutionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59486/1/ntu-95-R93221023-1.pdf