Variational formulation of the earth's elastic-gravitational deformations under low regularity conditions

On the system of elastic-gravitational equations describing the oscillations of the earth

The linear equations of motion of a uniformly rotating, elastic and self-gravitating earth model are analyzed under minimal regularity assumptions. We present existence and uniqueness results for the system, energy estimates, convergence of Galerkin approximations, and propose a method based on a Volterra equation to deal with the nonlocal self-gravitation.

弹性波系统的低正则性局部适定性

Low-Regularity Local Well-Posedness for the Elastic Wave System

本文研究三维弹性波系统，通过将动力学分解为散度部分和旋度部分，首次证明了具有多个波速的波系统在最优低正则性条件下的局部适定性。

Low regularity ill-posedness for elastic waves driven by shock formation

In this paper, we construct counterexamples to the local existence of low-regularity solutions to elastic wave equations in three spatial dimensions (3D). Inspired by the recent works of Christodoulou, we generalize Lindblad's classic results on the scalar wave equation by showing that the Cauchy problem for 3D elastic waves, a physical system with multiple wave-speeds, is ill-posed in $H^3(\mathbb{R}^3)$. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. The main difficulties of the 3D …

A model for dislocations in epitaxially strained elastic films

A variational model for epitaxially strained films accounting for the presence of dislocations is considered. Existence, regularity and some qualitative properties of solutions are addressed.

用Colombeau函数进行地球物理模拟：微局部性质和Zygmund正则性

Geophysical modelling with Colombeau functions: Microlocal properties and Zygmund regularity

在全球地震学中，地球具有分形性质。Zygmund类似乎是测量这种局部分形性的最合适和最系统的方法。对于地震波传播的目的，我们模拟地球的性质作为Colombeau广义函数。在一维空间中，我们得到了Colombeau代数中Zygmund正则性的精确刻画。这是可能的，通过之间的关系软化和小波。

Regularity and energy transfer for a nonlinear beam equation

In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a spectral decomposition method we show that the main effects induced by the nonlinearity at the transition from attached to detached states can be traced in a loss of regularity of the solution and in a migration of the total energy through the scales.