具有不完备特征向量集的2 × 2非保守系统的奇异解
Singular solutions for a 2X2 system in nonconservative form with incomplete set of eigenvectors
摘要：
本文研究两个非保守形式的一阶系统的初值问题。第一个系统出现在弹性动力学，属于严格双曲，真正的非线性系统类。第二个系统有重复的特征值和一个不完整的右特征向量集。这种系统的解决方案预计将开发奇异浓度。利用弱渐近方法证明了这两个系统的奇异解的存在性。第二个系统已被证明发展奇异浓度，甚至从黎曼型初始数据。第一个系统与第二个系统的不同之处在于有一个包含正常数k的额外项，当k趋于0时，为第一个系统构造的解已被证明收敛于第二个系统的解。
英文摘要：
In this paper, we study the initial-value problem for two first order systems in non-conservative form. The first system arises in elastodynamics and belongs to the class of strictly hyperbolic, genuinely nonlinear systems. The second system has repeated eigenvalues and an incomplete set of right eigenvectors. Solutions to such systems are expected to develop singular con- centrations. Existence of singular solutions to both the systems have been shown using the method of weak asymptotics. The second system has been shown to develop singular concentrations even from Riemann-type initial data. The first system differing from the second in having an extra term containing a positive constant k, the solution constructed for the first system have been shown to converge to the solution of the second as k tends to 0.
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