Mechanics is a branch of physics studying motion. The history of mechanics, as well as the
history of other branches of science, is a history of attempts to explain the world by means of …

Periodic Homogenization of Elliptic Systems Page 1 Operator Theory Advances and
Applications 269 Zhongwei Shen Periodic Homogenization of Elliptic Systems Page 2 Page 3 …

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial
differential equations with slow and fast time scales, or large and small spatial scales. The …

In this chapter we first consider turbulence from a somewhat heuristic viewpoint, in particular
discussing the importance of turbulence as a physical phenomenon and describing the main …

The purpose of this paper is to give an upscaling tool valid for the wave equation in general
elastic media. This paper is focused on P–SV wave propagation in 2-D, but the methodology …

Let Γ⊂ ℝ d be a lattice. For 𝜀> 0, we consider the perforated space Π 𝜀⊂ ℝ d which is an
(𝜀 Γ)-periodic open connected set with Lipschitz boundary. In L 2 (Π 𝜀; ℂ n), we consider a …

Homogenization is an important mathematical framework for developing effective models of
differential equations with oscillations. We include in the presentation techniques for …

When considering numerical acoustic or elastic wave propagation in media containing small
heterogeneities with respect to the minimum wavelength of the wavefield, being able to …

The book is based on the authors' results on asymptotic approximations of Green's kernels
for elliptic boundary value problems in perforated domains. A new feature is the uniformity of …

We consider an infinite planar straight strip perforated by small holes along a curve. In such
a domain, we consider a general second-order elliptic operator subject to classical …