层状多孔弹性介质中波传播的解析解。部件II：3D案例

简正波分解与分层流体中的色散和非线性混合

Normal mode decomposition and dispersive and nonlinear mixing in stratified fluids

本文从分析分层海洋中内波传播的角度出发，考虑变密度不可压欧拉方程组，研究了密度稳定垂直分层时流体静力平衡扰动的演化。我们显示在这种配置的方程的局部适定性，并提供了详细的研究，他们的线性逼近。根据与背景分层相关的Sturm-Liouville问题进行模态分解，我们证明了线性逼近可以由线性波动方程的一系列色散扰动来描述。当所谓的Brunt-Vais{ä}l{ä}频率不是常数时，我们证明了这些方程是耦合的，从而表现出色散混合现象。然后，我们考虑更具体的浅水配置（当水平尺度比深度大得多时）;在Boussinesq近似下（即忽略动量方程中的密度变化），我们提供了一个适定性定理，我们能够根据相关的物理尺度控制存在时间。然后，我们可以将模态分解扩展到非线性情况，并表现出与上述色散混合不同性质的非线性混合。最后，我们讨论了一些观点，如尖锐的分层限制，预计将收敛到两个流体系统。

分层类地球模式中的全球声日光成像

Global acoustic daylight imaging in a stratified Earth-like model

我们提出了一个类似地球的模型，假设一个广义过程的噪声源空间上支持在一个环形远离表面的声学日光成像的分析。我们假设标量波传播的情况下，测量的波场在表面。然后，我们得到的测量值的自相关函数和由一个脉冲源产生的散射场的轨迹之间的关系定位在地表下。从这个关系，例如，很明显，本征频率可以从自相关恢复。此外，完全散射算子可以提取的附加假设下，环是接近的表面，并具有小于的典型波长的厚度。

水声波与海啸传播的适定性与基于势的公式化

Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis

研究分层自由表面海洋中水声波与海啸传播的线性模型，通过分析函数空间和算子提出更易数学研究和高效离散化的新公式化，证明两种公式化的适定性，并用谱元法模拟海底地震和滑坡引发的海啸。

Homogenization for a Variational Problem with a Slip Interface Condition

Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic composites. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip interface condition posed on the micro-scale. However, for certain pore fluids, the no-slip conditions are known to be physically invalid. Even though there are results in a few papers regarding porous media with slip condition on the interface, they are for porous media with rigid solid matrix rather than an elastic one. For the former case, the equations for the…

Propagation of singularities for the wave equation on manifolds with corners

In this paper we describe the propagation of smooth (C^\infty) and Sobolev singularities for the wave equation on smooth manifolds with corners M equipped with a Riemannian metric g. That is, for X=MxR, P=D_t^2-Δ_M, and u locally in H^1 solving Pu=0 with homogeneous Dirichlet or Neumann boundary conditions, we show that the wave front set of u is a union of maximally extended generalized broken bicharacteristics. This result is a smooth counterpart of Lebeau's results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary. Our methods re…