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
具线性退化特征场对角型方程组Goursat问题的奇性形成机制
Mechanism of the Formation of Singularities to the Goursat Problem for Diagonal Systems with Linearly Degenerate Characteristic Fields
投稿时间:2010-11-02  最后修改时间:2010-11-20
DOI:10.3770/j.issn:1000-341X.2011.01.003
中文关键词:  奇性形成  Goursat 问题  整体 $C^1$ 解  对角型拟线性双曲组  线性退化特征  弱间断解.
英文关键词:formation of singularity  Goursat problem  global $C^1$ solution  quasilinear hyperbolic system of diagonal form  linearly degenerate characteristic  weakly discontinuous solution.
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).
作者单位
杨永富 河海大学理学院数学系, 江苏 南京 210098 
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中文摘要:
      对于对角型的拟线性双曲组, 若假设系统为线性退化及边界值的 $C^1$ 模有界, 证明了在原点满足 $C^1$ 相容性假设的Goursat 问题的奇性形成机制为 ODE 型. 对原点满足 $C^0$ 相容性假设的弱间断解也得到了类似的结果.
英文摘要:
      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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