论文标题
线性化中耦合方程式的准方程系统的库奇问题
The Cauchy problem for a quasilinear system of equations with coupling in the linearization
论文作者
论文摘要
用线性化和固定点的方法解决了双曲 - 羟基方程式的准线性系统的Cauchy问题。在线性化中允许双曲线和抛物线变量之间的耦合，我们不假定弗里德里奇的系统对称性。这种耦合导致线性能量估计，以防止Banach收缩原理的应用。为了结论解决方案的局部存在和独特性，开发了度量固定点定理。我们表明，通过引入解决方案图的封闭延伸概念，可以将高标准和低标准中的收缩界的界限纳入固定点的配方中。我们将结果应用于Cattaneo-Christov系统的粘性压缩流体流，这是一个方程系统，其无粘性部分不是双曲线。
The Cauchy problem for a quasilinear system of hyperbolic-parabolic equations is addressed with the method of linearization and fixed point. Coupling between the hyperbolic and parabolic variables is allowed in the linearization and we do not assume the Friedrich's symmetrizability of the system. This coupling results in linear energy estimates that prevent the application of Banach's contraction principle. A metric fixed point theorem is developed in order to conclude the local existence and uniqueness of solutions. We show that the boundedness in the high norm and contraction in the low norm can be incorporated into the formulation of the fixed point by introducing the notion of a closed extension of the solution map. We apply our results to the Cattaneo-Christov system for viscous compressible fluid flow, a system of equations whose inviscid part is not hyperbolic.
