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

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.

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.