FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEM 被引量：4

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEM

导出

摘要 The author gets a blow-up result of C^1 solution to the Cauchy problem for a first order quasilinear non-strlctly hyperbolic system in one space dimension. The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.

作者 WANG LIBINInstitute of Mathematics, Fudan University, Shanghai 200433, China.

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2002年第4期439-454,共16页 数学年刊（B辑英文版）

关键词奇异性构造拟线性非严格双曲系统 CAUCHY问题特征值胀开弱线性退化解 Formation of singularity, Quasilinear non-strictly hyperbolic system, Weak linear degeneracy

分类号 O175.27 [理学—基础数学]

引文网络
相关文献

参考文献3

1YAN PING Institute of Mathematics, Fudan University, Shanghai 200433, China.GLOBAL CLASSICAL SOLUTIONS WITH SMALL INITIAL TOTAL VARIATION FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2002,23(3):335-348. 被引量：5
2QIN TIEHU.A CONSTITUTIVE EQUATION SATISFYING THE NULL CONDITION FOR NONLINEAR COMPRESSIBLE ELASTICITY[J].Chinese Annals of Mathematics,Series B,2002,23(4):435-438. 被引量：3
3KONG DEXING (Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, China.).LIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATALIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATA[J].Chinese Annals of Mathematics,Series B,2000,21(4):413-440. 被引量：14

二级参考文献3

1XIN JIE Institute of Mathematics, Laboratory of Mathematics for Nonlinear Sciences, Pudan University, Shanghai 200433, China..SOME REMARKS ON THE NULL CONDITION FOR NONLINEAR ELASTODYNAMIC SYSTEM[J].Chinese Annals of Mathematics,Series B,2002,23(3):311-316. 被引量：2
2LI TA-TSIEN (LI DAQIAN), JIN YI Department of Mathematics, Fudan University, Shanghai 200433, China..SEMI-GLOBAL C^1 SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2001,22(3):325-336. 被引量：31
3KONG DEXING (Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, China.).LIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATALIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATA[J].Chinese Annals of Mathematics,Series B,2000,21(4):413-440. 被引量：14

共引文献18

1LITATSIEN,WANGLIBIN.GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NON-SMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2004,25(3):319-334. 被引量：10
2WangLibin.CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS WITH CHARACTERISTICS WITH CONSTANT MULTIPLICITY[J].Journal of Partial Differential Equations,2004,17(3):221-240.
3XINJIE,QINTIEHU.ALMOST GLOBAL EXISTENCE OF DIRICHLETINITIAL-BOUNDARY VALUE PROBLEM FORNONLINEAR ELASTODYNAMIC SYSTEMOUTSIDE A STAR-SHAPED DOMAIN[J].Chinese Annals of Mathematics,Series B,2004,25(4):433-454.
4闫萍,盛其荣,吕腾.线性退化的严格双曲组具慢衰减初值的Cauchy问题的经典解的整体存在唯一性[J].数学物理学报（A辑）,2005,25(4):473-481.
5Tatsien LI.Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case[J].Chinese Annals of Mathematics,Series B,2006,27(1):53-66. 被引量：1
6杨雄锋.拟线性双曲方程组经典解存在区间的下界(英文)[J].数学杂志,2006,26(3):237-242. 被引量：1
7Wenrong DAI.Asymptotic Behavior of Global Classical Solutions of Quasilinear Non-strictly Hyperbolic Systems with Weakly Linear Degeneracy[J].Chinese Annals of Mathematics,Series B,2006,27(3):263-286. 被引量：3
8Xu Yumei Dept. of Math., Qufu Normal Univ., Shandong 273165, China,School of Math. Sci., Fudan Univ., Shanghai 200433, China..BREAKDOWN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS[J].Applied Mathematics(A Journal of Chinese Universities),2006,21(4):437-453.
9徐玉梅.BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS[J].数学物理学报（A辑）,2006,26(B12):1089-1104.
10闫萍.具小全变差拟线性双曲组的整体经典解(英文)[J].新疆大学学报（自然科学版）,2007,24(1):22-30.

同被引文献7

1LITATSIEN,WANGLIBIN.GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NON-SMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2004,25(3):319-334. 被引量：10
2Han Weiwei.GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE CAUCHY PROBLEM ON A SEMI-BOUNDED INITIAL AXIS FOR INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEMS[J].Journal of Partial Differential Equations,2007,20(3):273-288. 被引量：2
3YAN PING Institute of Mathematics, Fudan University, Shanghai 200433, China.GLOBAL CLASSICAL SOLUTIONS WITH SMALL INITIAL TOTAL VARIATION FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2002,23(3):335-348. 被引量：5
4QIN TIEHU.A CONSTITUTIVE EQUATION SATISFYING THE NULL CONDITION FOR NONLINEAR COMPRESSIBLE ELASTICITY[J].Chinese Annals of Mathematics,Series B,2002,23(4):435-438. 被引量：3
5WANGWEIKE,YANGXIONGFENG.POINTWISE ESTIMATES OF SOLUTIONS TO CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2003,24(4):457-468. 被引量：3
6KONG DEXING (Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, China.).LIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATALIFE-SPAN OF CLASSICAL SOLUTIONSTO QUASILINEAR HYPERBOLIC SYSTEMSWITH SLOW DECAY INITIAL DATA[J].Chinese Annals of Mathematics,Series B,2000,21(4):413-440. 被引量：14
7ZHOUYI.GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY[J].Chinese Annals of Mathematics,Series B,2004,25(1):37-56. 被引量：19

引证文献4

1LITATSIEN,WANGLIBIN.GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NON-SMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Chinese Annals of Mathematics,Series B,2004,25(3):319-334. 被引量：10
2徐玉梅.BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS[J].数学物理学报（A辑）,2006,26(B12):1089-1104.
3Guo Fei School of Mathematical Sciences, Fudan University, Shanghai 200433, China,Department of Mathematics, Qufu Normal University, Shandong, 273165, China..GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Applied Mathematics(A Journal of Chinese Universities),2007,22(2):181-200. 被引量：2
4Wei Wei HAN1,2 1. Department of Applied Mathematics, Donghua University, Shanghai 201620, P. R. China,2. School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China.Asymptotic Behavior of Global Classical Solutions to the Cauchy Problem on a Semi-Bounded Initial Axis for Quasilinear Hyperbolic Systems[J].Journal of Mathematical Research and Exposition,2010,30(1):41-53. 被引量：1

二级引证文献13

1武佩霞.一阶非齐次拟线性双曲组的柯西问题整体经典解的存在性[J].数学年刊（A辑）,2006,27(1):93-108. 被引量：1
2Tatsien LI.Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case[J].Chinese Annals of Mathematics,Series B,2006,27(1):53-66. 被引量：1
3徐玉梅,张海军.具常重特征拟线性非严格双曲组的经典解的奇性形成(英文)[J].工程数学学报,2006,23(4):571-589. 被引量：1
4郭飞.具一种非光滑初始数据的非齐次拟线性双曲组的整体弱间断解(英文)[J].工程数学学报,2007,24(3):414-430. 被引量：1
5Guo Fei School of Mathematical Sciences, Fudan University, Shanghai 200433, China,Department of Mathematics, Qufu Normal University, Shandong, 273165, China..GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS[J].Applied Mathematics(A Journal of Chinese Universities),2007,22(2):181-200. 被引量：2
6Wei Wei HAN1,2 1. Department of Applied Mathematics, Donghua University, Shanghai 201620, P. R. China,2. School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China.Asymptotic Behavior of Global Classical Solutions to the Cauchy Problem on a Semi-Bounded Initial Axis for Quasilinear Hyperbolic Systems[J].Journal of Mathematical Research and Exposition,2010,30(1):41-53. 被引量：1
7殷宗芳.一阶拟线性严格双曲型方程组弱间断解的精确能控性及能观性[J].工程数学学报,2010,27(6):1041-1050.
8Yong Fu YANG.Mechanism of the Formation of Singularities to the Goursat Problem for Diagonal Systems with Linearly Degenerate Characteristic Fields[J].Journal of Mathematical Research and Exposition,2011,31(1):23-33.
9XianchaoWANG,Chengshun JIANG.Asymptotic Behavior of a Non-Local Hyperbolic Equation Modelling Ohmic Heating[J].Journal of Mathematical Research with Applications,2012,32(4):476-484.
10Fei GUO.Global Weakly Discontinuous Solutions for Inhomogeneous Quasilinear Hyperbolic Systems with Characteristics with Constant Multiplicity[J].Journal of Mathematical Research with Applications,2012,32(6):699-714.

1徐玉梅.BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS[J].数学物理学报（A辑）,2006,26(B12):1089-1104.
2Huang Feimin Institute of Applied Mathematics, Academic. Sinica, Beijing 100080, China.On the Two-Dimensional Cauchy Problem of a Hyperbolic System[J].Acta Mathematica Sinica,English Series,1998,14(3):399-410.
3PeterY.H.Pang,TangHongyan,WangYoude.NONLINEAR SCHROEDINGER EQUATIONS WITH VARIABLE COEFFICIENTS—BLOWUP[J].Journal of Partial Differential Equations,2003,16(2):189-192.
4JIU Quansen(Department of Mathematics, Capital Normal University, Beijing 100037, China).NONHOMOGENEOUS HOPF EQUATIONS IN HIGHER DIMENSIONS[J].Systems Science and Mathematical Sciences,1999,12(2):115-122.
5Jiaxin Hu Wuhan Institute of Physics and Mathematics, Academia Sinica, P.O.Box 71010, Wuhan 430071, P. R. China CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France.A Two-Dimensional Hyperbolic System of Nonlinear Conservation Laws with Functional Solutions[J].Acta Mathematica Sinica,English Series,1999,15(3):317-332.
6AbbesBenaissa,Salim.A.Messaoud.BLOW－UP OF SOLUTIONS OF A QUASILINEAR WAVE EQUATION WITH NONLINEAR DISSIPATION[J].Journal of Partial Differential Equations,2002,15(3):61-67. 被引量：1
7Shuxing Chen Yi Zhou Institute of Mathematics,Fudan University,Shanghai 200433,P.R.China E-mail:sxchen@fudan.ac.cn Fax:021-65646073.Decay Rate of Solutions to Hyperbolic System of First Order[J].Acta Mathematica Sinica,English Series,1999,15(4):471-484.
8丁夏畦,王振.Existence and uniqueness of discontinuous solutions defined by Lebesgue-Stieltjes integral[J].Science China Mathematics,1996,39(8):807-819. 被引量：4
9ChenGuowang.INITIAL BOUNDARY VALUE PROBLEM FOR A DAMPED NONLINEAR HYPERBOLIC EQUATION[J].Journal of Partial Differential Equations,2003,16(1):49-61. 被引量：8
10栗付才,陈有朋,谢春红.ASYMPTOTIC BEHAVIOR OF SOLUTION FOR NONLOCAL REACTION-DIFFUSION SYSTEM[J].Acta Mathematica Scientia,2003,23(2):261-273. 被引量：8

Chinese Annals of Mathematics,Series B

2002年第4期

浏览历史

内容加载中请稍等...