丽水学院学报
麗水學院學報
려수학원학보
Journal of Lishui University
2015年
5期
10-14
,共5页
非线性波动方程%位势%破裂%生命跨度
非線性波動方程%位勢%破裂%生命跨度
비선성파동방정%위세%파렬%생명과도
nonlinear wave equation%potential%blow up%life span
带位势项的非线性波动方程解的大时间行为与空间维数、非线性项的指数有着密切的联系.当非线性项的指数与空间维数满足一定关系时,将证明小初值Cauchy问题的解在有限时间内破裂.进一步,将建立解的生命跨度上界估计.
帶位勢項的非線性波動方程解的大時間行為與空間維數、非線性項的指數有著密切的聯繫.噹非線性項的指數與空間維數滿足一定關繫時,將證明小初值Cauchy問題的解在有限時間內破裂.進一步,將建立解的生命跨度上界估計.
대위세항적비선성파동방정해적대시간행위여공간유수、비선성항적지수유착밀절적련계.당비선성항적지수여공간유수만족일정관계시,장증명소초치Cauchy문제적해재유한시간내파렬.진일보,장건립해적생명과도상계고계.
The long-time behavior of the solutions to nonlinear wave equations with potential largely dependson the dimension and the power of the nonlinear term. In this paper,we establish the blow-up result of thesmall data Cauchy problem of nonlinear wave equations with potential,assuming that the exponent of thenonlinear term satisfies some condition. Furthermore,we obtain the upper bound of the life span.
