四川师范大学学报（自然科学版）
四川師範大學學報（自然科學版）
사천사범대학학보（자연과학판）
JOURNAL OF SICHUAN NORMAL UNIVERSITY(NATURAL SCIENCE)
2011年
1期
110-122,封2
,共14页
重新尺度化的Klein-Cordon-Zakharov系统%整体解%交叉强制变分方法%交叉不变流形
重新呎度化的Klein-Cordon-Zakharov繫統%整體解%交扠彊製變分方法%交扠不變流形
중신척도화적Klein-Cordon-Zakharov계통%정체해%교차강제변분방법%교차불변류형
rescaled Klein-Cordon-Zakhalov system%global existence%cross-constrained variational method%cross-invariant manifold
提出一类交叉强制变分法来研究二维和三维空间中一类重新尺度化的Klein-Gordon-Zakharov系统的整体解.通过构造一类交叉强制变分问题,引入该系统柯西问题解流下的不变流形并利用伸缩变换,得到了该系统柯西问题解存在的一个充分条件.这个充分条件蕴涵着对于某些大初值,该系统柯西问题的整体解也存在.此外,证明了两个小初值准则,其回答了当初值为多小时,该系统柯西问题的整体解存在这个问题.
提齣一類交扠彊製變分法來研究二維和三維空間中一類重新呎度化的Klein-Gordon-Zakharov繫統的整體解.通過構造一類交扠彊製變分問題,引入該繫統柯西問題解流下的不變流形併利用伸縮變換,得到瞭該繫統柯西問題解存在的一箇充分條件.這箇充分條件蘊涵著對于某些大初值,該繫統柯西問題的整體解也存在.此外,證明瞭兩箇小初值準則,其迴答瞭噹初值為多小時,該繫統柯西問題的整體解存在這箇問題.
제출일류교차강제변분법래연구이유화삼유공간중일류중신척도화적Klein-Gordon-Zakharov계통적정체해.통과구조일류교차강제변분문제,인입해계통가서문제해류하적불변류형병이용신축변환,득도료해계통가서문제해존재적일개충분조건.저개충분조건온함착대우모사대초치,해계통가서문제적정체해야존재.차외,증명료량개소초치준칙,기회답료당초치위다소시,해계통가서문제적정체해존재저개문제.
We present a cross-constrained variational method to discuss the global solution of the rescaled Klein-Cordon-Zakharov svstem in two and three space dimensions.By constructing a type of cross-constrained variational problem,accomplishing so-called cross-invariant manifolds under the solution flow of the Cauehy problem of the Klein-Cordon-Zakharov system and using skillful dilation transformation,we give a sufficient condition on the global existence of solution to the Cauchy problem for the Klein-Cordon-Zakhalov system.The sufficient condition implies that for some large Cauchy data,the solution of the Cauchy problem for the Klein-Gordon-Zakharov system may exist globally.Furthermore,we obtain two small data criteria which answer the question:how small are the initial data, the solution to the Cauchy problem of the Klein-Gordon-Zakharov system exists globally?
