@article{45964,
abstract = {{Abstract
Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal $L^p$-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal $L^p$-regularity is used to prove the boundedness and stability of numerical solutions in the $L^\infty (0,T;W^{1,\infty })$ norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the $L^\infty (0,T;W^{1,\infty })$ norm is obtained by combining the stability analysis with the consistency estimates.}},
author = {{Kovács, Balázs and Li, Buyang}},
issn = {{0272-4979}},
journal = {{IMA Journal of Numerical Analysis}},
keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
publisher = {{Oxford University Press (OUP)}},
title = {{{Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems}}},
doi = {{10.1093/imanum/drac033}},
year = {{2022}},
}
@article{45966,
abstract = {{Abstract
This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk–surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form $\tau \leqslant c h$ for some constant $c>0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type.}},
author = {{Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}},
issn = {{0272-4979}},
journal = {{IMA Journal of Numerical Analysis}},
keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
number = {{2}},
pages = {{950--975}},
publisher = {{Oxford University Press (OUP)}},
title = {{{Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions}}},
doi = {{10.1093/imanum/drac002}},
volume = {{43}},
year = {{2022}},
}
@article{45968,
abstract = {{Abstract
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.}},
author = {{Csomós, Petra and Farkas, Bálint and Kovács, Balázs}},
issn = {{0272-4979}},
journal = {{IMA Journal of Numerical Analysis}},
keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
publisher = {{Oxford University Press (OUP)}},
title = {{{Error estimates for a splitting integrator for abstract semilinear boundary coupled systems}}},
doi = {{10.1093/imanum/drac079}},
year = {{2022}},
}
@article{45958,
abstract = {{AbstractIn this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.}},
author = {{Beschle, Cedric Aaron and Kovács, Balázs}},
issn = {{0029-599X}},
journal = {{Numerische Mathematik}},
keywords = {{Applied Mathematics, Computational Mathematics}},
number = {{1}},
pages = {{1--48}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces}}},
doi = {{10.1007/s00211-022-01280-5}},
volume = {{151}},
year = {{2022}},
}
@article{45956,
abstract = {{Abstract
The full Maxwell equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials.
We propose a weak formulation of the coupled system based on the boundary integral formulation of the exterior Maxwell equations.
We show existence and partial uniqueness of a weak solution and propose a new numerical algorithm based on finite elements and boundary elements as spatial discretization with backward Euler and convolution quadrature for the time domain.
This is the first numerical algorithm which is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and full Maxwell’s equations without any simplifications like quasi-static approximations (e.g. eddy current model) and without restrictions on the shape of the domain (e.g. convexity).
We show well-posedness and convergence of the numerical algorithm under minimal assumptions on the regularity of the solution.
This is particularly important as there are few regularity results available and one generally expects the solution to be non-smooth.
Numerical experiments illustrate and expand on the theoretical results.}},
author = {{Bohn, Jan and Feischl, Michael and Kovács, Balázs}},
issn = {{1609-4840}},
journal = {{Computational Methods in Applied Mathematics}},
keywords = {{Applied Mathematics, Computational Mathematics, Numerical Analysis}},
number = {{1}},
pages = {{19--48}},
publisher = {{Walter de Gruyter GmbH}},
title = {{{FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation}}},
doi = {{10.1515/cmam-2022-0145}},
volume = {{23}},
year = {{2022}},
}
@inbook{53174,
author = {{Krause, Ina}},
booktitle = {{ZBW-Beiheft: Betriebliche Berufsbildungsforschung}},
editor = {{Bellmann, Lutz and Ertl, Hubert and Gerhards, Christian and Sloane, Peter}},
title = {{{Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie}}},
year = {{2022}},
}
@inbook{33740,
author = {{KOUAGOU, N'Dah Jean and Heindorf, Stefan and Demir, Caglar and Ngonga Ngomo, Axel-Cyrille}},
booktitle = {{The Semantic Web}},
isbn = {{9783031069802}},
issn = {{0302-9743}},
publisher = {{Springer International Publishing}},
title = {{{Learning Concept Lengths Accelerates Concept Learning in ALC}}},
doi = {{10.1007/978-3-031-06981-9_14}},
year = {{2022}},
}
@article{53266,
author = {{Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard A.}},
issn = {{0018-9545}},
journal = {{IEEE Transactions on Vehicular Technology}},
keywords = {{Electrical and Electronic Engineering, Computer Networks and Communications, Aerospace Engineering, Automotive Engineering}},
number = {{4}},
pages = {{4580--4597}},
publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}},
title = {{{Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling}}},
doi = {{10.1109/tvt.2022.3222633}},
volume = {{72}},
year = {{2022}},
}
@article{53267,
author = {{Soleymani, Mohammad and Santamaria, Ignacio and Schreier, Peter J.}},
issn = {{2473-2400}},
journal = {{IEEE Transactions on Green Communications and Networking}},
keywords = {{Computer Networks and Communications, Renewable Energy, Sustainability and the Environment}},
number = {{2}},
pages = {{723--738}},
publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}},
title = {{{Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance}}},
doi = {{10.1109/tgcn.2021.3140150}},
volume = {{6}},
year = {{2022}},
}
@inbook{53306,
author = {{Mohammadi, Hassan Ghasemzadeh and Jentzsch, Felix Paul and Kuschel, Maurice and Arshad, Rahil and Rautmare, Sneha and Manjunatha, Suraj and Platzner, Marco and Boschmann, Alexander and Schollbach, Dirk}},
booktitle = {{Communications in Computer and Information Science}},
isbn = {{9783030937355}},
issn = {{1865-0929}},
publisher = {{Springer International Publishing}},
title = {{{FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics}}},
doi = {{10.1007/978-3-030-93736-2_27}},
year = {{2022}},
}
@article{53319,
abstract = {{Abstract
The Neumann problem for (0.1)$$ \begin{align}& V_t = \Delta V-aV+f(x,t) \end{align}$$is considered in bounded domains $\Omega \subset {\mathbb {R}}^n$ with smooth boundary, where $n\ge 1$ and $a\in {\mathbb {R}}$. By means of a variational approach, a statement on boundedness of the quantities $$ \begin{eqnarray*} \sup_{t\in (0,T)} \int_\Omega \big|\nabla V(\cdot,t)\big|^p L^{\frac{n+p}{n+2}} \Big( \big|\nabla V(\cdot,t)\big| \Big) \end{eqnarray*}$$in dependence on the expressions (0.2)$$ \begin{align}& \sup_{t\in (0,T-\tau)} \int_t^{t+\tau} \int_\Omega |f|^{\frac{(n+2)p}{n+p}} L\big( |f|\big) \end{align}$$is derived for $p\ge 2$, $\tau>0$, and $T\ge 2\tau $, provided that $L\in C^0([0,\infty ))$ is positive, strictly increasing, unbounded, and slowly growing in the sense that $\limsup _{s\to \infty } \frac {L(s^{\lambda _0})}{L(s)} <\infty $ for some $\lambda _0>1$. In the particular case when $p=n\ge 2$, an additional condition on growth of $L$, particularly satisfied by $L(\xi ):=\ln ^\alpha (\xi +b)$ whenever $b>0$ and $\alpha>\frac {(n+2)(n-1)}{2n}$, is identified as sufficient to ensure that as a consequence of the above, bounds for theintegrals in (0.2) even imply estimates for the spatio-temporal modulus of continuity of solutions to (0.1). A subsequent application to the Keller–Segel system $$ \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \nabla \cdot \big( D(v)\nabla u\big) - \nabla \cdot \big( uS(v)\nabla v\big) + ru - \mu u^2, \\[1mm] v_t = \Delta v-v+u, \end{array} \right. \end{eqnarray*}$$shows that when $n=2$, $r\in {\mathbb {R}}$, $0<D\in C^2([0,\infty ))$, and $S\in C^2([0,\infty )) \cap W^{1,\infty }((0,\infty ))$ and thus especially in the presence of arbitrarily strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\mu>0$ excludes blowup in the sense that for all suitably regular nonnegative initial data, an associated initial-boundary value problem admits a global bounded classical solution.}},
author = {{Winkler, Michael}},
issn = {{1073-7928}},
journal = {{International Mathematics Research Notices}},
keywords = {{General Mathematics}},
number = {{19}},
pages = {{16336--16393}},
publisher = {{Oxford University Press (OUP)}},
title = {{{A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System}}},
doi = {{10.1093/imrn/rnac286}},
volume = {{2023}},
year = {{2022}},
}
@article{53321,
abstract = {{ The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text], [Formula: see text], where the positive function [Formula: see text] reflects suitably weak diffusion by satisfying [Formula: see text] for some [Formula: see text]. It is shown that whenever [Formula: see text] is positive and satisfies [Formula: see text] as [Formula: see text], one can find a suitably regular nonlinearity [Formula: see text] with the property that at each sufficiently large mass level [Formula: see text] there exists a globally defined radially symmetric classical solution to a Neumann-type boundary value problem for (⋆) which satisfies [Formula: see text] }},
author = {{Winkler, Michael}},
issn = {{0219-1997}},
journal = {{Communications in Contemporary Mathematics}},
keywords = {{Applied Mathematics, General Mathematics}},
number = {{10}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems}}},
doi = {{10.1142/s0219199722500626}},
volume = {{25}},
year = {{2022}},
}
@article{53323,
abstract = {{AbstractIn a ball $$\Omega =B_R(0)\subset \mathbb {R}^n$$
Ω
=
B
R
(
0
)
⊂
R
n
, $$n\ge 2$$
n
≥
2
, the chemotaxis system $$\begin{aligned} \left\{ \begin{array}{l}u_t = \nabla \cdot \big ( D(u) \nabla u \big ) - \nabla \cdot \big ( uS(u)\nabla v\big ), \\ 0 = \Delta v - \mu + u, \qquad \mu =\frac{1}{|\Omega |} \int _\Omega u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$
u
t
=
∇
·
(
D
(
u
)
∇
u
)
-
∇
·
(
u
S
(
u
)
∇
v
)
,
0
=
Δ
v
-
μ
+
u
,
μ
=
1
|
Ω
|
∫
Ω
u
,
(
⋆
)
is considered under no-flux boundary conditions, with a focus on nonlinearities $$S\in C^2([0,\infty ))$$
S
∈
C
2
(
[
0
,
∞
)
)
which exhibit super-algebraically fast decay in the sense that with some $$K_S>0, \beta \in [0,1)$$
K
S
>
0
,
β
∈
[
0
,
1
)
and $$\xi _0>0$$
ξ
0
>
0
, $$\begin{aligned} S(\xi )>0 \quad \text{ and } \quad S'(\xi ) \le -K_S\xi ^{-\beta } S(\xi ) \qquad \text{ for } \text{ all } \xi \ge \xi _0. \end{aligned}$$
S
(
ξ
)
>
0
and
S
′
(
ξ
)
≤
-
K
S
ξ
-
β
S
(
ξ
)
for
all
ξ
≥
ξ
0
.
It is, inter alia, shown that if furthermore $$D\in C^2((0,\infty ))$$
D
∈
C
2
(
(
0
,
∞
)
)
is positive and suitably small in relation to S by satisfying $$\begin{aligned} \frac{\xi S(\xi )}{D(\xi )} \ge K_{SD}\xi ^\lambda \qquad \text{ for } \text{ all } \xi \ge \xi _0 \end{aligned}$$
ξ
S
(
ξ
)
D
(
ξ
)
≥
K
SD
ξ
λ
for
all
ξ
≥
ξ
0
with some $$K_{SD}>0$$
K
SD
>
0
and $$\lambda >\frac{2}{n}$$
λ
>
2
n
, then throughout a considerably large set of initial data, ($$\star $$
⋆
) admits global classical solutions (u, v) fulfilling $$\begin{aligned} \frac{z(t)}{C} \le \Vert u(\cdot ,t)\Vert _{L^\infty (\Omega )} \le Cz(t) \qquad \text{ for } \text{ all } t>0, \end{aligned}$$
z
(
t
)
C
≤
‖
u
(
·
,
t
)
‖
L
∞
(
Ω
)
≤
C
z
(
t
)
for
all
t
>
0
,
with some $$C=C^{(u,v)}\ge 1$$
C
=
C
(
u
,
v
)
≥
1
, where z denotes the solution of $$\begin{aligned} \left\{ \begin{array}{l}z'(t) = z^2(t) \cdot S\big ( z(t)\big ), \qquad t>0, \\ z(0)=\xi _0, \end{array} \right. \end{aligned}$$
z
′
(
t
)
=
z
2
(
t
)
·
S
(
z
(
t
)
)
,
t
>
0
,
z
(
0
)
=
ξ
0
,
which is seen to exist globally, and to satisfy $$z(t)\rightarrow +\infty $$
z
(
t
)
→
+
∞
as $$t\rightarrow \infty $$
t
→
∞
. As particular examples, exponentially and doubly exponentially decaying S are found to imply corresponding infinite-time blow-up properties in ($$\star $$
⋆
) at logarithmic and doubly logarithmic rates, respectively.}},
author = {{Winkler, Michael}},
issn = {{1040-7294}},
journal = {{Journal of Dynamics and Differential Equations}},
keywords = {{Analysis}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Slow Grow-up in a Quasilinear Keller–Segel System}}},
doi = {{10.1007/s10884-022-10167-w}},
year = {{2022}},
}
@article{53327,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
keywords = {{Analysis, Applied Mathematics}},
pages = {{390--418}},
publisher = {{Elsevier BV}},
title = {{{Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension}}},
doi = {{10.1016/j.jde.2022.10.022}},
volume = {{343}},
year = {{2022}},
}
@article{53325,
author = {{Desvillettes, Laurent and Laurençot, Philippe and Trescases, Ariane and Winkler, Michael}},
issn = {{0362-546X}},
journal = {{Nonlinear Analysis}},
keywords = {{Applied Mathematics, Analysis}},
publisher = {{Elsevier BV}},
title = {{{Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing}}},
doi = {{10.1016/j.na.2022.113153}},
volume = {{226}},
year = {{2022}},
}
@article{53331,
abstract = {{In a ball $\Omega \subset \mathbb {R}^{n}$ with $n\ge 2$, the chemotaxis system
\[ \left\{ \begin{array}{@{}l} u_t = \nabla \cdot \big( D(u)\nabla u\big) + \nabla\cdot \big(\dfrac{u}{v} \nabla v\big), \\ 0=\Delta v - uv \end{array} \right. \]is considered along with no-flux boundary conditions for $u$ and with prescribed constant positive Dirichlet boundary data for $v$. It is shown that if $D\in C^{3}([0,\infty ))$ is such that $0< D(\xi ) \le {K_D} (\xi +1)^{-\alpha }$ for all $\xi >0$ with some ${K_D}>0$ and $\alpha >0$, then for all initial data from a considerably large set of radial functions on $\Omega$, the corresponding initial-boundary value problem admits a solution blowing up in finite time.}},
author = {{Wang, Yulan and Winkler, Michael}},
issn = {{0308-2105}},
journal = {{Proceedings of the Royal Society of Edinburgh: Section A Mathematics}},
keywords = {{General Mathematics}},
number = {{4}},
pages = {{1150--1166}},
publisher = {{Cambridge University Press (CUP)}},
title = {{{Finite-time blow-up in a repulsive chemotaxis-consumption system}}},
doi = {{10.1017/prm.2022.39}},
volume = {{153}},
year = {{2022}},
}
@article{53344,
abstract = {{ A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. }},
author = {{Winkler, Michael}},
issn = {{1664-3607}},
journal = {{Bulletin of Mathematical Sciences}},
keywords = {{General Mathematics}},
number = {{02}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}}},
doi = {{10.1142/s1664360722500126}},
volume = {{13}},
year = {{2022}},
}
@techreport{35788,
author = {{Fochmann, Martin and Heinemann-Heile, Vanessa and Huber, Hans-Peter and Maiterth, Ralf and Sureth-Sloane, Caren}},
issn = {{1556-5068}},
keywords = {{General Earth and Planetary Sciences, General Environmental Science}},
title = {{{Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)}}},
doi = {{10.2139/ssrn.4210460}},
volume = {{100}},
year = {{2022}},
}
@techreport{35795,
author = {{Greil, Stefan and Overesch, Michael and Rohlfing-Bastian, Anna and Schreiber, Ulrich and Sureth-Sloane, Caren}},
issn = {{1556-5068}},
title = {{{Towards an Amended Arm's Length Principle - Tackling complexity and implementing destination rules in transfer pricing}}},
doi = {{10.2139/ssrn.4166972}},
volume = {{89}},
year = {{2022}},
}
@inproceedings{52574,
author = {{Werth, Gerda}},
booktitle = {{Beiträge zum Mathematikunterricht}},
location = {{Frankfurt am. Main}},
publisher = {{WTM}},
title = {{{Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings}}},
doi = {{https://doi.org/10.37626/GA9783959872089.0}},
year = {{2022}},
}