How far away is the harmonic mean from the homogenized matrix
Marcus Waurick · arXiv (Cornell University) · 2012
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and give a unified treatment for (non-)periodic homogenization problems in thermodynamics, elasticity, electro-magnetism and coupled systems thereof. The approach permits the consideration of memory problems. We show that the limiting equation is well-posed and causal and prove that the principal physical phenomenon remains unchanged after the homogenization process. The results should be read as of a mere structural nature: We show what homogenization problems discussed in the literature may have in common. We only rely on techniques from functional analysis and operator theory.