Abstract Concerning the global existence of classical solution to systems of hyperbolic-parabolic composite type, a well-known general theory was established by Kawashima in [4] , where the dissipation condition (Kawashima-Shizuta condition) to the linearized system plays a fundamental role. Recently, systems with much weaker dissipations have attracted a lot of attentions, see [1] , [2] , [10] , [11] among others. The typical feature of this kind of system is that the corresponding linearized system has one eigenvalue with the real part equals to zero. This violates the Kawashima-Shizuta stability conditions. In this paper, we develop a general global well-posedness theory for this kind of system. Moreover, as the applications of the general theory, several examples are given.

中文翻译：

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具有中心流形的双曲-抛物线复合型系统的全局适定性

摘要 关于双曲-抛物线复合型系统经典解的全局存在性，Kawashima 在 [4] 中建立了著名的一般理论，其中对线性化系统的耗散条件（Kawashima-Shizuta 条件）起基本作用。 . 最近，具有更弱耗散的系统引起了很多关注，参见[1]、[2]、[10]、[11]等。这种系统的典型特征是相应的线性化系统具有一个实部为零的特征值。这违反了 Kawashima-Shizuta 稳定条件。在本文中，我们为这种系统开发了一个通用的全局适定性理论。此外，作为一般理论的应用，给出了几个例子。