On the effect of oil-trapping and the derivation of a homogenized equation: Oiltrapping2008. This regards the two-phase flow equations in a one-dimensional domain with an interface condition at (many) internal interfaces.

A system with forward- and backward diffusion: Backward2008. This talk is about a  scalar equation in one space dimension, including diffusion with both signs. Together with D. Horstmann I compared two different solution concepts and characterized one of them with a free boundary problem.

Outflow boundary conditions for various porous media equations: Outflow2009. For various bulk equations (degenerate and non-degenerate Richards, two-phase flow) a regularization scheme for outflow boundary conditions is analyzed. Results are in parts obtained together with M. Lenzinger and S. Pop.

Homogenization of hysteresis problems: Hysteresis2010. This presentation regards homogenization methods for problems with hysteresis which could be applied to Hydromechanics and to Plasticity.

Plasticity: Homogenization of plasticity equations is presented e.g. in Plasticity-Rome-2016

Meta-Materials are studied in the context of Maxwell equations. Together with G. Bouchitte and later with A. Lamacz I studied the question whether materials with a negative optical index can be constructed with a complex micro-structure. Indeed, such a construction was proposed by Pendry and others. In our contribution we give a detailed analysis of the microscopic behavior of electric and magnetic field and derive an effective Maxwell equation with negative index. A related effect is perfect transmission.  MetaMat2013

Fingering effect for Richards equation with hysteresis: Fingering2013. When we introduce static hysteresis in the Richards equation, planar front solutions become unstable. Together with the dynamic term, true fingering occurs for both Richards and two-phase flow in porous media under the influence of gravity.

Dispersion for  waves in heterogeneous materials: Waves2015. We describe waves with a linear wave equation, the elliptic operator is in divergence form and with highly oscillatory coefficients. For finite times, the effective equation is again a linear second order wave equation -- and cannot describe the dispersion effects that are observed numerically and experimentally. Instead, for large times, the effective equation is a dispersive wave equation

Representation with profile functions: At large times, the solution of a wave equation can be represented as a ring (or shell) with a profile function that solves an easy equation Representation-SIAM-2022.