11 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…
The Closed Range Property and Gaffney's Inequality of the De Rham Complex in Unbounded Domains
Dirk Pauly, Marcus Waurick
The classical Poincaré estimate establishes closedness of the range of the gradient in unweighted -spaces as long as is contained in a slab, that i…
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…
Block operator matrix techniques for stability properties of hyperbolic equations
Marcus Waurick
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a bl…
Exponential Stability for Maxwell-type Systems Revisited
Marcus Waurick
Considering a two-by-two block operator matrix system of Maxwell type, we present an elementary way of deducing exponential stability under minimal smoothness (and boundedness) req…