Abstract

This paper is devoted to a simpler derivation of energy estimates and a proof of the well-posedness, compared to previously existing ones, for effectively hyperbolic Cauchy problem. One difference is that instead of using the general Fourier integral operator, we only use a change of local coordinates x (of the configuration space) leaving the time variable invariant. Another difference is an efficient application of the Weyl-Hörmander calculus of pseudodifferential operators associated with several different metrics.

中文翻译：

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有效双曲算子的柯西问题的更直接方法

摘要

与之前存在的方法相比，本文致力于更简单地推导能量估计，并证明有效双曲柯西问题的适定性。一个区别是，我们不使用一般的傅里叶积分算子，而是仅使用（配置空间的）局部坐标x的变化，从而使时间变量保持不变。另一个区别是与多个不同度量相关的伪微分算子的 Weyl-Hörmander 演算的有效应用。