21 citations · 35 across the 13 of their papers we have counts for
14 papers
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…
Analysis of coupled Maxwell-cable problems
Timo Reis, Nathanael Skrepek
Building on the recently published work "Modeling of radiating curved cables via coupled telegrapher's and Maxwell's equations", which introduces a model for the interaction betwee…
Modeling of radiating curved cables via coupled telegrapher's and Maxwell's equations
Markus Clemens, Michael Günther, Timo Reis +1
We investigate the electromagnetic interactions of cable harnesses in the time domain. We present a novel model that allows for curved cables, extending the standard assumptions ty…
Well-posedness and stability of the Lagrange representation of the n-D wave equation via boundary triples
Bernhard Aigner, Nathanael Skrepek
We study the Lagrange representation of the wave equation with generalized Laplacian . We allow the coefficients -- the Young modulus and the densi…
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…
Semi-uniform stabilization of anisotropic Maxwell's equations via boundary feedback on split boundary
Nathanael Skrepek, Marcus Waurick
We regard anisotropic Maxwell's equations as a boundary control and observation system on a bounded Lipschitz domain. The boundary is split into two parts: one part with perfect co…
Weak Operator Continuity for Evolutionary Equations
Andreas Buchinger, Nathanael Skrepek, Marcus Waurick
Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping fr…
Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains
Nathanael Skrepek, Dirk Pauly
We investigate the boundary trace operators that naturally correspond to , namely the tangential and twisted tangential trace, where $Ω\subseteq…
Characterizations of the Sobolev space on the boundary of a strong Lipschitz domain in 3-D
Nathanael Skrepek
In this work we investigate the Sobolev space on a strong Lipschitz boundary , i.e., is a strong Lipschitz domain. In most of the literat…
Quasi Gelfand triples
Nathanael Skrepek
We generalize the notion of Gelfand triples (also called Banach-Gelfand triples or rigged Hilbert spaces) by dropping the necessity of a continuous embedding. This means in our set…
Mixed-Dimensional Geometric Coupling of Port-Hamiltonian Systems
Jens Jäschke, Nathanael Skrepek, Matthias Ehrhardt
We propose a new interconnection relation for infinite-dimensional port-Hamiltonian systems that enables the coupling of ports with different spatial dimensions by integrating over…
Stability of the multidimensional wave equation in port-Hamiltonian modelling
Birgit Jacob, Nathanael Skrepek
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedba…
A Compactness Result for the div-curl System with Inhomogeneous Mixed Boundary Conditions for Bounded Lipschitz Domains and Some Applications
Dirk Pauly, Nathanael Skrepek
For a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any -bounded sequence of vector fields with -bounded rotations and $L^2…
Well-posedness of linear first order Port-Hamiltonian Systems on multidimensional spatial domains
Nathanael Skrepek
We consider a port-Hamiltonian system on a spatial domain that is bounded with Lipschitz boundary. We show that there is a boundary triple associated to t…