RIEMANN-HILBERT PROBLEMS OF DEGENERATE HYPERBOLIC SYSTEM

RIEMANN-HILBERT PROBLEMS OF DEGENERATE HYPERBOLIC SYSTEM

导出

摘要 This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented. This paper is concerned with the Riemann-Hilbert problems of degenerate hyperbolic system in two general domains, where the boundary curves are given by the parameter equations of the arc length s. We prove the existence and uniqueness of solutions to the Riemann-Hilbert problems by conformal deformations. The corre-sponding representations of solutions to the problems are also presented.

作者 Zhongtai Ma, Guangshan Xu (School of Math., Shandong Institute of Business & Technology, Yantai 264005, Shandong)

出处《Annals of Differential Equations》 2010年第2期200-205,共6页 微分方程年刊（英文版）

基金 Supported by the NSF of Shandong Province (Y2008A31)

关键词 Riemann-Hilbert problem degenerate hyperbolic system deforma-tion of hyperbolic domain uniqueness and existence Riemann-Hilbert problem degenerate hyperbolic system deforma-tion of hyperbolic domain uniqueness and existence

分类号 O175.27 [理学—基础数学]

引文网络
相关文献

参考文献17

1G. Barantsev.On singularities of the tricomi problem solution by the fourier method. Teubner- Texte zur Mathematik, Leipzig . 1986
2S.A. Chaplygin.One case of vortex motion in ffuid. Trans. Phys. Sect. Imperial Moscow Soc. Friends of Natural Sci . 1903
3S.A. Chaplygin.Gas jets, Complete Works. . 1933
4F.I. Frankl.On the problems of Chaplygin for mixed subsonic and supersonic ffows. Izv. Akad. Nauk SSSR Ser. Mat . 1945
5Z. Ma,D. Ma.Discontinuous oblique derivative problems for second order quasilinear mixed equations in general domains. Applied Mathematics and Computation . 2004
6R.I. Semerdjieva.Uniqueness of regular solutions for a class of non-linear degenerating hyper- bolic equations. Math. Balk . 1993
7G. Wen.Boundary value problems for degenerate hyperbolic system of first order equations. Complex Vari . 2002
8M.H. Protter.Uniqueness theorems for the Tricomi problem II. J. Rat. Mech. Anal . 1955
9Wen G C.Linear and Quasilinear Complex Equations of Hyperbolic and Mixed type. . 2002
10Bitsadze A V.Differential Equations of Mixed Type. . 1964

1Huang 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.
2Ping ZhangInstitute of Mathematics,Chinese Academy of Sciences,Beijing 100080,P.R.ChinaYuxi ZhengDepartment of Mathematics,Indiana University,Bloomington,Indiana 47405 USA.On the Existence and Uniqueness of Solutions to an Asymptotic Equation of a Variational Wave Equation[J].Acta Mathematica Sinica,English Series,1999,15(1):115-129. 被引量：2
3Xin Ying XU Jun Ning ZHAO.On the Global Existence and Uniqueness of Solutions to Prandtl's System[J].Acta Mathematica Sinica,English Series,2009,25(1):109-132.
4Jiaxin 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.
5徐振远.ON LINEAR AND NONLINEAR RIEMANN-HILBERT PROBLEMS FOR REGULAR FUNCTION WITH VALUES IN A CLIFFORD ALGEBRA[J].Chinese Annals of Mathematics,Series B,1990,11(3):349-357. 被引量：14
6Conformal deformation of a close Riemannian submanifold to minimal submanifold[J].Chinese Science Bulletin,1998,43(6):527-527.
7武际可,许为厚,丁红丽.ARC-LENGTH METHOD FOR DIFFERENTIAL EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),1999,20(8):115-121.
8Shuxing 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.
9XU Hongmei,WANG Weike.A Linear Hyperbolic System with Stiff Source Terms[J].Wuhan University Journal of Natural Sciences,2007,12(2):207-210.
10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：5

Annals of Differential Equations

2010年第2期

浏览历史

内容加载中请稍等...

RIEMANN-HILBERT PROBLEMS OF DEGENERATE HYPERBOLIC SYSTEM

参考文献17

相关作者

相关机构

相关主题

浏览历史