4 papers · 1 filter
Nonlinear Media via Nonlocal Homogenisation
Andreas Buchinger, Nathanael Skrepek, Marcus Waurick
We consider a nonlinear PDE describing a nonlinear electrostatic medium with nonlocal dielectricity. The existence proof for the corresponding equation is based on Schauder's theor…
The Free Lunch Theorem of Homogenisation
Andreas Buchinger, Marianna Porfido, Marcus Waurick
We show that H-convergence for multiplication type operators as envisioned by Murat and Tartar in the 1970's always implies nonlocal H-convergence as introduced in 2018 in Calc.~Va…
Avscon the Schur topology
Andreas Buchinger, Marcus Waurick
The aim of the course is to lead to an understanding of homogenisation processes in an operator-theoretic sense. In fact, using solely operator-theoretic means not referring to the…
Characterisation of homogenisation for nonlocal diffusion by local topologies
Andreas Buchinger, Krešimir Burazin, Ivana Crnjac +3
We consider fractional variants of divergence form problems with highly oscillatory local coefficients. We characterise the convergence of these coefficients by means of classical…