6 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…
Duality for Evolutionary Equations with Applications to Null Controllability
Andreas Buchinger, Christian Seifert
We study evolutionary equations in exponentially weighted -spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe…
Homogenisation for Maxwell and Friends
Andreas Buchinger, Sebastian Franz, Nathanael Skrepek +1
We refine the understanding of continuous dependence on coefficients of solution operators under the nonlocal -topology viz Schur topology in the setting of evolutionary equatio…