ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

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摘要 This paper is a continuation of the authors' previous paper [1]. In this paper the authors prove, assuming additional conditions on the initial data, some results about the existence and uniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolic system

作者 J.P.DIAS M.FIGUEIRA

机构地区 Dedicated to the memory of Jacques-Louis Lions

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2002年第3期317-324,共8页 数学年刊（B辑英文版）

基金 Project supported by the FCT and FEDER

关键词 Cauchy problem Weak solution Quasilinear hyperbolic system 唯一性弱熵解拟线性双曲系统奇异源项 Cauchy问题 Riemann边分抛物系统

分类号 O175.29 [理学—基础数学]

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1Dias,J.P.& Figueira,M.,On the radial weak solutionsof a conservative system modeling the isentropic flow [J],Rendic.di Mat.,21(2001),245-258.
2DiPerna,R.J.,Convergence of approximate solutions to conservation laws [J],Arch.Rat.Mech.Anal.,82(1983),27-70.
3DiPerna,R.J.,Convergence of the viscosity method for isentropic gas dynamics [J],Commun.Math.Phys.,91(1983),1-30.
4Godlewski,E.& Raviart,P.A.,Hyperbolic systems of conservation laws [M],Mathématiques et Applications,SMAI,Ellipses,1991.
5Kruzkov,S.N.,First order quasilinear equations in several independent variables [J],Math.USSR Sbornik,10(1970),217-243.
6Schonbek,M.E.,Existence of solutions to singular conservation laws [J],SlAM J.Math.Anal.,15(1984),1125-1139.
7Whitham,G.B.,Linear and nonlinear waves [M],Wiley Interscience,New York,1974.

1黄维章.对角型拟线性双曲系统在大初值下整体光滑解的存在性[J].应用数学学报,1991,14(2):229-233. 被引量：1
2韦真,杨永富.2×2线性退化系统初边值问题的显式解（英文）[J].复旦学报（自然科学版）,2017,56(1):34-39.
3罗李平,罗振国,曾云辉.一类带阻尼项的拟线性双曲系统的(全)振动性问题[J].山东大学学报（理学版）,2016,51(6):73-77.
4Steave C. Selvaduray.On a Quasilinear Hyperbolic System Relative to an Atmospheric Model on the Transition of Water Defined on the Whole Space[J].Journal of Mathematics and System Science,2014,4(9):637-655.
5薛晓琳,刘存明.拟线性双曲型方程组Cauchy问题行波解的稳定性[J].数学学报（中文版）,2016,59(6):745-760.
6李书敏.CAUCHY PROBLEM FOR GENERAL FIRST ORDER INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEMS[J].Journal of Partial Differential Equations,2002,15(1):46-68. 被引量：4
7罗李平,罗振国,曾云辉.带脉冲效应的拟线性双曲系统(强)振动性分析[J].山东大学学报（理学版）,2015,50(3):57-61. 被引量：2
8陈宇,周忆.SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS[J].Acta Mathematica Scientia,2015,35(4):855-875. 被引量：2
9Wei Wei HAN.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.
10Xiang CHEN.Lipschitz Continuous Solutions to the Cauchy Problem for Quasi-linear Hyperbolic Systems[J].Chinese Annals of Mathematics,Series B,2012,33(4):521-536.

Chinese Annals of Mathematics,Series B

2002年第3期

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ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

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