对称双曲系统的复几何光学I：线性理论
Complex geometric optics for symmetric hyperbolic systems I: linear theory
摘要：
我们获得了线性一阶对称双曲型方程组Cauchy问题的$\ep \to 0$的渐近解，该方程组的振荡初值用几何光学的程函形式表示，频率为$1/\ep$，但相位复杂。对于最常见的线性波传播模型，这类柯西问题在应用文献中是众所周知的，并且它们的渐近理论，称为复几何光学，正在吸引应用的兴趣。这项工作是致力于非线性对称双曲系统的复杂几何光学的系列论文中的第一篇，我们建立了严格的线性理论，并为随后的非线性分析奠定了基础。
英文摘要：
We obtain an asymptotic solution for $\ep \to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\ep$, but with complex phases. For the most common linear wave propagation models, this kind on Cauchy problems are well-known in the applied literature and their asymptotic theory, referred to as complex geometric optics, is attracting interest for applications. In this work, which is the first of a series of papers dedicated to complex geometric optics for nonlinear symmetric hyperbolic systems, we develop a rigorous linear theory and set the basis for the subsequent nonlinear analysis.
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