| 具线性退化特征场对角型方程组Goursat问题的奇性形成机制 |
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| 引用本文： | 杨永富.具线性退化特征场对角型方程组Goursat问题的奇性形成机制[J].数学研究及应用,2011,31(1):23-33. |
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| 作者姓名： | 杨永富 |
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| 作者单位： | 河海大学理学院数学系, 江苏 南京 210098 |
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| 基金项目： | 国家自然科学基金(Grant No.10926162),中央高校基本科研业务费(Grant No.2009B01314),河海大学自然科学基金(Grant No.2009428011). |
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| 摘 要： | For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.
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| 关 键 词： | formation of singularity Goursat problem global C^1 solution quasilinear hyper- bolic system of diagonal form linearly degenerate characteristic weakly discontinuous solution. |
| 收稿时间： | 2010/11/2 0:00:00 |
| 修稿时间： | 2010/11/20 0:00:00 |
Mechanism of the Formation of Singularities to the Goursat Problem for Diagonal Systems with Linearly Degenerate Characteristic Fields |
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| Yong 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 with Applications,2011,31(1):23-33. |
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| Authors: | Yong Fu YANG |
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| Institution: | Department of Mathematics,College of Sciences,Hohai University,Jiangsu 210098,P.R.China |
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| Abstract: | For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the $C^1$ norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of $C^1$ classical solution to the Goursat problem with $C^1$ compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with $C^0$ compatibility conditions at the origin. |
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| Keywords: | formation of singularity Goursat problem global $C^1$ solution quasilinear hyperbolic system of diagonal form linearly degenerate characteristic weakly discontinuous solution |
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