一种全频散波方程的反问题

The inverse problem of a full dispersive wave equation

基于一种全频散波方程研究了对于谐波和波包的反问题。首先根据Mindlin理论建立了描述无耗散微结构线性固体中波传播模型一一种全频散波方程,并讨论了其频散特性。然后基于该全频散波方程,提出了利用四种不同谐波的频率和相应波数确定波方程四个未知系数的反问题,并用严格的数学理论论证了此反问题。研究证明,通过测量同一种无耗散微结构线性固体中传播的四种不同谐波的频率和相应波数,在正常频散和反常频散情况下可唯一地确定波方程的未知系数,即材料的未知参数。

The inverse problem for harmonic waves and wave packets was studied based on a full dispersive wave equation. First, a full dispersive wave equation which describes wave propagation in nondissipative microstructured linear solids is established based on the Mindlin theory, and the dispersion characteristics are discussed. Second, based on the full dispersive wave equation, an inverse problem for determining the four unknown coefficients of wave equation is posed in terms of the frequencies and corresponding wave numbers of four different harmonic waves, and the inverse problem is demonstrated with rigorous mathematical theory. Research proves that the coefficients of wave equation related to material properties can be uniquely determined in cases of normal and anomalous dispersions by measuring the frequencies and corresponding wave numbers of four different harmonic waves which propagate in a nondissipative microstructured linear solids.