On the Nonlinear Riemann Problems for General First Elliptic Systems in the Plane

LI Ming-zhong; SONG Jie

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LI Ming-zhong, SONG Jie. On the Nonlinear Riemann Problems for General First Elliptic Systems in the Plane[J]. Applied Mathematics and Mechanics, 2005, 26(1): 72-76.

Citation:

LI Ming-zhong, SONG Jie. On the Nonlinear Riemann Problems for General First Elliptic Systems in the Plane[J]. Applied Mathematics and Mechanics, 2005, 26(1): 72-76.

Citation:

LI Ming-zhong, SONG Jie. On the Nonlinear Riemann Problems for General First Elliptic Systems in the Plane[J]. Applied Mathematics and Mechanics, 2005, 26(1): 72-76.

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On the Nonlinear Riemann Problems for General First Elliptic Systems in the Plane

LI Ming-zhong¹,
SONG Jie²

1.
Mathematics Department, Shanghai University, Shanghai 200072, P. R. China;

Received Date: 2002-12-29
Rev Recd Date: 2004-10-08
Publish Date: 2005-01-15

Abstract

Abstract

The nonlinear Riemann problem for general systems of two first order linear and quasi-linear equations in the plane are considered.It translates them to singular integral equations and proves the existence of the solution by means of contract principle or general contract principle.The known results are generalized.
- Riemann problem,
- elliptic system,
- singular integral equation

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References(7)

References

[1]	宋洁，李明忠.双解析函数的线性和非线性Riemann边值问题[A].见：程昌钧，戴世强，刘宇陆主编.现代数学和力学(Ⅷ)[C].上海：上海大学出版社，1997，533—538.
[2]	Abduhamid Dzhuraev,Lasisa Kopp.On the Riemann problem for general first order elliptic systems in the plane[J].Complex Variables,1992,18(2):109—118. doi: 10.1080/17476939208814535
[3]	Vekua I N.Generalized Analytic Functions[M].Oxford:Pergamon,1962.
[4]	李明忠，温晓琴.一般形式的一阶椭圆型偏微分方程组拟线性Riemann-Hilbert问题[J].数学年刊，A辑，2002，23(1)：13—20.
[5]	侯宗义，李明忠，张万国.奇异积分方程理论及其应用[M].上海：上海科技大学出版社，1990.
[6]	李明忠，侯宗义，徐振远.椭圆型方程组理论和边值问题[M].上海：复旦大学出版社，1990.
[7]	Wolfersdorf L V.A class of nonlinear Riemann-Hilbert problems for holomorphic functions[J].Math Nachr,1984,116(1):89—107. doi: 10.1002/mana.19841160108