The damped wave equation with the attenuation proportional to velocity is ubiquitous in science and engineering and a common situation is when the attenuation depends on frequency. The usual way to incorporate this effect is to introduce fractional order derivatives either as a replacement for u _t or as modifier through a spatial component with space fractional derivatives. Models for these are very well developed and the effort in this paper is towards the analysis of the inverse problem of recovering critical coefficients or initial states although we also develop constructive methods for these and analyse their degree of ill-conditioning.

中文翻译：

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分数阶导数衰减的波动方程的一些反问题

在科学和工程中，衰减与速度成比例的衰减波方程是普遍存在的，并且常见的情况是衰减取决于频率。将这一效果的常用方法是要么介绍分数阶导数作为用于替换ü _吨或作为通过与空间分数衍生物一个空间分量改性剂。这些模型非常完善，尽管我们也为这些问题开发了构造方法并分析了它们的病态程度，但本文的工作是致力于分析恢复临界系数或初始状态的反问题。