6 papers
A variational perspective on auxetic metamaterials of checkerboard-type
Wolf-Patrick Düll, Dominik Engl, Carolin Kreisbeck
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of phy…
Analysis of the embedded cell method for the numerical homogenization of metal-ceramic composite materials
Wolf-Patrick Düll, Bastian Hilder, Guido Schneider
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the conver…
The KdV, the Burgers, and the Whitham limit for a spatially periodic Boussinesq model
Roman Bauer, Wolf-Patrick Düll, Guido Schneider
We are interested in the Korteweg-de Vries (KdV), the Burgers, and the Whitham limit for a spatially periodic Boussinesq model with non-small contrast. We prove estimates between t…
Existence of long time solutions and validity of the Nonlinear Schrödinger approximation for a quasilinear dispersive equation
Wolf-Patrick Düll, Max Heß
We consider a nonlinear dispersive equation with a quasilinear quadratic term. We establish two results. First, we show that solutions to this equation with initial data of order $…
The validity of Whitham's approximation for a Klein-Gordon-Boussinesq model
Wolf-Patrick Düll, Kourosh Sanei Kashani, Guido Schneider
In this paper we prove the validity of a long wave Whitham approximation for a system consisting of a Boussinesq equation coupled with a Klein-Gordon equation. The proof is based o…
Justification of the Nonlinear Schrödinger approximation for a quasilinear Klein-Gordon equation
Wolf-Patrick Düll
We consider a nonlinear Klein-Gordon equation with a quasilinear quadratic term. The Nonlinear Schrödinger (NLS) equation can be derived as a formal approximation equation describi…