电子科技大学学报
電子科技大學學報
전자과기대학학보
JOURNAL OF UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA
2005年
2期
269-272
,共4页
调和势%非线性Schrodinger方程%爆破%能量守衡
調和勢%非線性Schrodinger方程%爆破%能量守衡
조화세%비선성Schrodinger방정%폭파%능량수형
nonlinear Schrodinger equation%harmonic potential%blow up%energy conservative
研究了一类带调和势的Schrodinger方程的解,运用能量守衡定律和质量守衡定律以及利用矢量分析的知识,引入积分不等式和解微分不等式的方法,得到了初值满足一定条件的柯西问题的解会在有限的时间里发生爆破的结论.由于所讨论方程更具有一般性,从而推广了已有的结论,所得到结论也可以对能量和质量的集中现象作进一步解释.
研究瞭一類帶調和勢的Schrodinger方程的解,運用能量守衡定律和質量守衡定律以及利用矢量分析的知識,引入積分不等式和解微分不等式的方法,得到瞭初值滿足一定條件的柯西問題的解會在有限的時間裏髮生爆破的結論.由于所討論方程更具有一般性,從而推廣瞭已有的結論,所得到結論也可以對能量和質量的集中現象作進一步解釋.
연구료일류대조화세적Schrodinger방정적해,운용능량수형정률화질량수형정률이급이용시량분석적지식,인입적분불등식화해미분불등식적방법,득도료초치만족일정조건적가서문제적해회재유한적시간리발생폭파적결론.유우소토론방정경구유일반성,종이추엄료이유적결론,소득도결론야가이대능량화질량적집중현상작진일보해석.
In the paper, a class of Schr(o)dinger equation with harmonic Potential, which concerns Bose-Einstin condensates, is investigated. Now that the equation of Bose-einstin condensates describes lot of phenomena, that we research it has special significance. With the help of using energy conservative law and quality conservative law as well as knowledge of vector analysis, integral and differential inequality, we prove that the solution to the Cauchy's problem will blow up in finite time in case initial value satisfy with some conditions. As the equation in the paper is more general, we have got extensive conclusion, by means of which we may deeply understand the aggregative phenomena on energy and quality.
