具有不可对角化的主部和可变重数的双曲型方程组，I。适定性
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posedness
摘要：
本文分析了一类具有时空不定常系数的双曲型方程组的Cauchy问题的适定性。首先，我们在各向异性索伯列夫空间中建立了具有上三角主部的系统在一些有趣的自然条件下关于对角线下低阶项的阶数的适定性结果.也就是说，对角线下方距离$k$的项必须是$-k$阶。该设置还允许系统中的Jordan块结构。其次，我们给出了一般变系数系统的Schur型三角化的条件，使其化为具有上三角主部的形式，从而使第一个结果可以应用。给出了$2\times 2$和$3\times 3$系统出现的条件和构造的详细说明，并通过几个例子加以补充.
英文摘要：
In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity. First, we establish a well-posedness result in anisotropic Sobolev spaces for systems with upper triangular principal part under interesting natural conditions on the orders of lower order terms below the diagonal. Namely, the terms below the diagonal at a distance $k$ to it must be of order $-k$. This setting also allows for the Jordan block structure in the system. Second, we give conditions for the Schur type triangularisation of general systems with variable coefficients for reducing them to the form with an upper triangular principal part for which the first result can be applied. We give explicit details for the appearing conditions and constructions for $2\times 2$ and $3\times 3$ systems, complemented by several examples.
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