ABSTRACT

In this paper, we analyze acoustic wave propagation in anisotropic fluids and solids. By formulating the acoustic system as an evolution equation over a Hilbert space, we obtain global in time solutions when the associated material parameters are bounded and measurable. In particular, we prove well-posedness of a Cauchy problem for wave propagation in piezoelectric crystals. We then provide a stability analysis of these solutions not assuming positive definiteness of the stress–strain tensor or the piezoelectric stress tensor. Finally we prove continuous dependence on initial data, allowing the piezoelectric tensor to depend on space and time, provided solutions belong to an appropriate function space.

摘要

在本文中，我们分析了声波在各向异性流体和固体中的传播。通过将声学系统公式化为希尔伯特空间上的演化方程，当相关材料参数有界且可测量时，我们获得了全局时间解。特别是，我们证明了压电晶体中波传播的柯西问题的适定性。然后，我们提供了这些解的稳定性分析，不假设应力-应变张量或压电应力张量的正定性。最后，我们证明了对初始数据的连续依赖，允许压电张量依赖于空间和时间，前提是解属于适当的函数空间。