LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u= u^k(u)~α 被引量：1

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u= u^k(u)~α

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摘要 This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H3 and Hs for semilinear wave equations with polynomial nonlinearity in u and (?)u. This ill-posed result concerns the focusing type equations with nonlinearity on u and (?)tu.

作者 FANGDAOYUAN WANGCHENGBO

机构地区 DepartmentofMathematics

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2005年第3期361-378,共18页 数学年刊（B辑英文版）

基金 Project supported by the National Natural Science Foundation of China (No.10271108).

关键词 Semilinear wave equation Low regularity Local well-posedness ILL-POSEDNESS 半线性波动函数低正则性非线性多项式柯西问题数学物理方程

分类号 O411.1 [理学—理论物理]

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参考文献1

1ZHOU YI Institute of Mathematics, Fudan University, Shanghai 200433, China..ON THE EQUATION□Φ=|▽Φ|~2 IN FOUR SPACE DIMENSIONS[J].Chinese Annals of Mathematics,Series B,2003,24(3):293-302. 被引量：2

二级参考文献13

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共引文献1

1XUERUYING,FANGDAOYUAN.GLOBAL EXISTENCE AND ASYMPTOTICS BEHAVIOR OF SOLUTIONS FOR A RESONANT KLEIN-GORDON SYSTEM IN TWO SPACE DIMENSIONS[J].Chinese Annals of Mathematics,Series B,2005,26(1):89-104.

同被引文献1

1ZHOU YI Institute of Mathematics, Fudan University, Shanghai 200433, China.BLOW UP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEAR WAVE EQUATIONS[J].Chinese Annals of Mathematics,Series B,2001,22(3):275-280. 被引量：19

引证文献1

1Meng Yun LIU,Cheng Bo WANG.Global Existence for Some 4-D Quasilinear Wave Equations with Low Regularity[J].Acta Mathematica Sinica,English Series,2018,34(4):629-640.

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2沈彩霞.非线性动力系统多项式首次积分的不存在性[J].广西科学院学报,2008,24(1):9-10.
3向雅捷.一维二阶非线性薛定谔方程的局部适定性[J].湖南文理学院学报（自然科学版）,2017,29(2):12-16. 被引量：2
4倪华,田立新.变量代换法和非线性多项式微分方程的通解(英文)[J].大学数学,2013,29(3):22-29. 被引量：1
5CUI Xiaona,DOU Changsheng,JIU Quansen.Local Well-Posedness and Blow Up Criterion for the Inviscid Boussinesq System in Holder Spaces[J].Journal of Partial Differential Equations,2012,25(3):220-238. 被引量：3
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7HuoZhaohui,GuoBoling.LOCAL WELL-POSEDNESS OF INTERACTION EQUATIONS FOR SHORT AND LONG DISPERSIVE WAVES[J].Journal of Partial Differential Equations,2004,17(2):137-151. 被引量：1
8贾红艳,王宏伟.OST方程初值问题的低正则性[J].安徽大学学报（自然科学版）,2016,40(6):10-14.
9Ji-jun LiuDepartment of Mathematics, Nanjing Normal University, Nanjing 210097, China & Department of Applied Mathematics, Southeast University, Nanjing 210018, China.Linearization Ill-Posedness for 2.5-D Ware Equation Inversion Model[J].Acta Mathematicae Applicatae Sinica,2002,18(2):219-230.
10李木华.二维空间中方程utt＋（-△）^nu＋qu=εf（u，ε）解的低正则性估计[J].乐山师范学院学报,2003,18(4):7-8.

Chinese Annals of Mathematics,Series B

2005年第3期

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