@article{53328,
abstract = {{ As a simplified version of a three-component taxis cascade model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource growth and on the initial nutrient signal concentration are identified which ensure the global existence of a global classical solution to the corresponding no-flux initial-boundary value problem. Moreover, under additional assumptions on the food production source these solutions are shown to be bounded, and to stabilize toward semi-trivial equilibria in the large time limit, respectively. }},
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0218-2025}},
journal = {{Mathematical Models and Methods in Applied Sciences}},
keywords = {{Applied Mathematics, Modeling and Simulation}},
number = {{01}},
pages = {{103--138}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers}}},
doi = {{10.1142/s0218202523500045}},
volume = {{33}},
year = {{2023}},
}
@article{53324,
author = {{Ahn, Jaewook and Winkler, Michael}},
issn = {{0944-2669}},
journal = {{Calculus of Variations and Partial Differential Equations}},
keywords = {{Applied Mathematics, Analysis}},
number = {{6}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system}}},
doi = {{10.1007/s00526-023-02523-5}},
volume = {{62}},
year = {{2023}},
}
@article{53329,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{1468-1218}},
journal = {{Nonlinear Analysis: Real World Applications}},
keywords = {{Applied Mathematics, Computational Mathematics, General Economics, Econometrics and Finance, General Engineering, General Medicine, Analysis}},
publisher = {{Elsevier BV}},
title = {{{Analysis of a chemotaxis-SIS epidemic model with unbounded infection force}}},
doi = {{10.1016/j.nonrwa.2022.103820}},
volume = {{71}},
year = {{2023}},
}
@article{53326,
author = {{Li, Genglin and Winkler, Michael}},
issn = {{1539-6746}},
journal = {{Communications in Mathematical Sciences}},
keywords = {{Applied Mathematics, General Mathematics}},
number = {{2}},
pages = {{299--322}},
publisher = {{International Press of Boston}},
title = {{{Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities}}},
doi = {{10.4310/cms.2023.v21.n2.a1}},
volume = {{21}},
year = {{2023}},
}
@article{53343,
abstract = {{Abstract
The Cauchy problem in
R
n
{{\mathbb{R}}}^{n}
,
n
≥
2
n\ge 2
, for
u
t
=
Δ
u
−
∇
⋅
(
u
S
⋅
∇
v
)
,
0
=
Δ
v
+
u
,
(
⋆
)
\begin{array}{r}\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}_{t}=\Delta u-\nabla \cdot \left(uS\cdot \nabla v),\\ 0=\Delta v+u,\end{array}\right.\hspace{2.0em}\hspace{2.0em}\hspace{2.0em}\left(\star )\end{array}
is considered for general matrices
S
∈
R
n
×
n
S\in {{\mathbb{R}}}^{n\times n}
. A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to
BUC
(
R
n
)
∩
L
p
(
R
n
)
{\rm{BUC}}\left({{\mathbb{R}}}^{n})\cap {L}^{p}\left({{\mathbb{R}}}^{n})
with some
p
∈
[
1
,
n
)
p\in \left[1,n)
, there exist
T
max
∈
(
0
,
∞
]
{T}_{\max }\in \left(0,\infty ]
and a uniquely determined
u
∈
C
0
(
[
0
,
T
max
)
;
BUC
(
R
n
)
)
∩
C
0
(
[
0
,
T
max
)
;
L
p
(
R
n
)
)
∩
C
∞
(
R
n
×
(
0
,
T
max
)
)
u\in {C}^{0}\left(\left[0,{T}_{\max });\hspace{0.33em}{\rm{BUC}}\left({{\mathbb{R}}}^{n}))\cap {C}^{0}\left(\left[0,{T}_{\max });\hspace{0.33em}{L}^{p}\left({{\mathbb{R}}}^{n}))\cap {C}^{\infty }\left({{\mathbb{R}}}^{n}\times \left(0,{T}_{\max }))
such that with
v
≔
Γ
⋆
u
v:= \Gamma \star u
, and with
Γ
\Gamma
denoting the Newtonian kernel on
R
n
{{\mathbb{R}}}^{n}
, the pair
(
u
,
v
)
\left(u,v)
forms a classical solution of (
⋆
\star
) in
R
n
×
(
0
,
T
max
)
{{\mathbb{R}}}^{n}\times \left(0,{T}_{\max })
, which has the property that
if
T
max
<
∞
,
then both
limsup
t
↗
T
max
‖
u
(
⋅
,
t
)
‖
L
∞
(
R
n
)
=
∞
and
limsup
t
↗
T
max
‖
∇
v
(
⋅
,
t
)
‖
L
∞
(
R
n
)
=
∞
.
\hspace{0.1em}\text{if}\hspace{0.1em}\hspace{0.33em}{T}_{\max }\lt \infty ,\hspace{1.0em}\hspace{0.1em}\text{then both}\hspace{0.1em}\hspace{0.33em}\mathop{\mathrm{limsup}}\limits_{t\nearrow {T}_{\max }}\Vert u\left(\cdot ,t){\Vert }_{{L}^{\infty }\left({{\mathbb{R}}}^{n})}=\infty \hspace{1.0em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspace{1.0em}\mathop{\mathrm{limsup}}\limits_{t\nearrow {T}_{\max }}\Vert \nabla v\left(\cdot ,t){\Vert }_{{L}^{\infty }\left({{\mathbb{R}}}^{n})}=\infty .
An exemplary application of this provides a result on global classical solvability in cases when
∣
S
+
1
∣
| S+{\bf{1}}|
is sufficiently small, where
1
=
diag
(
1
,
…
,
1
)
{\bf{1}}={\rm{diag}}\hspace{0.33em}\left(1,\ldots ,1)
.}},
author = {{Winkler, Michael}},
issn = {{2391-5455}},
journal = {{Open Mathematics}},
keywords = {{General Mathematics}},
number = {{1}},
publisher = {{Walter de Gruyter GmbH}},
title = {{{Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type}}},
doi = {{10.1515/math-2022-0578}},
volume = {{21}},
year = {{2023}},
}
@article{53345,
abstract = {{AbstractA no-flux initial-boundary value problem forut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered in smoothly bounded subdomains ofRnwithn⩾1and suitably regular initial data, whereφis assumed to reflect algebraic type cross-degeneracies by sharing essential features with0⩽ξ↦ξαfor someα⩾1. Based on the discovery of a gradient structure acting at regularity levels mild enough to be consistent with degeneracy-driven limitations of smoothness information, in this general setting it is shown that with some measurable limit profileu∞and some null setN⋆⊂(0,∞), a corresponding global generalized solution, known to exist according to recent literature, satisfiesρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1as(0,∞)∖N⋆∋t→∞, whereρ(ξ):=ξ2(ξ+1)2,ξ⩾0. In the particular case when eithern⩽2andα⩾1is arbitrary, orn⩾1andα∈[1,2], additional quantitative information on the deviation of trajectories from the initial data is derived. This is found to imply a lower estimate for the spatial oscillation of the respective first components throughout evolution, and moreover this is seen to entail that each of the uncountably many steady states(u⋆,0)of (⋆) is stable with respect to a suitably chosen norm topology.}},
author = {{Winkler, Michael}},
issn = {{0951-7715}},
journal = {{Nonlinearity}},
keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}},
number = {{8}},
pages = {{4438--4469}},
publisher = {{IOP Publishing}},
title = {{{Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}}},
doi = {{10.1088/1361-6544/ace22e}},
volume = {{36}},
year = {{2023}},
}
@article{53341,
abstract = {{AbstractThe Cauchy problem in $$\mathbb {R}^n$$
R
n
is considered for the Keller–Segel system $$\begin{aligned} \left\{ \begin{array}{l}u_t = \Delta u - \nabla \cdot (u\nabla v), \\ 0 = \Delta v + u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$
u
t
=
Δ
u
-
∇
·
(
u
∇
v
)
,
0
=
Δ
v
+
u
,
(
⋆
)
with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data $$u_0$$
u
0
with non-integrable behavior at spatial infinity. It is shown that if $$u_0$$
u
0
is continuous and bounded, then ($$\star $$
⋆
) admits a local-in-time classical solution, whereas if $$u_0(x)\rightarrow +\infty $$
u
0
(
x
)
→
+
∞
as $$|x|\rightarrow \infty $$
|
x
|
→
∞
, then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in ($$\star $$
⋆
) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.}},
author = {{Winkler, Michael}},
issn = {{2296-9020}},
journal = {{Journal of Elliptic and Parabolic Equations}},
keywords = {{Applied Mathematics, Numerical Analysis, Analysis}},
number = {{2}},
pages = {{919--959}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity}}},
doi = {{10.1007/s41808-023-00230-y}},
volume = {{9}},
year = {{2023}},
}
@article{53339,
abstract = {{The chemotaxis‐Stokes system
is considered along with homogeneous boundary conditions of no‐flux type for
and
, and of Dirichlet type for
, in a smoothly bounded domain
. Under the assumption that
, that
is bounded on each of the intervals
with arbitrary
, and that with some
and
, we have
It is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution.}},
author = {{Tian, Yu and Winkler, Michael}},
issn = {{0170-4214}},
journal = {{Mathematical Methods in the Applied Sciences}},
keywords = {{General Engineering, General Mathematics}},
number = {{14}},
pages = {{15667--15683}},
publisher = {{Wiley}},
title = {{{Keller–Segel–Stokes interaction involving signal‐dependent motilities}}},
doi = {{10.1002/mma.9419}},
volume = {{46}},
year = {{2023}},
}
@article{53340,
author = {{Painter, Kevin J. and Winkler, Michael}},
issn = {{0036-1399}},
journal = {{SIAM Journal on Applied Mathematics}},
keywords = {{Applied Mathematics}},
number = {{5}},
pages = {{2096--2117}},
publisher = {{Society for Industrial & Applied Mathematics (SIAM)}},
title = {{{Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}}},
doi = {{10.1137/22m1539393}},
volume = {{83}},
year = {{2023}},
}
@article{53342,
author = {{Winkler, Michael and Yokota, Tomomi}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
keywords = {{Analysis, Applied Mathematics}},
pages = {{1--28}},
publisher = {{Elsevier BV}},
title = {{{Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems}}},
doi = {{10.1016/j.jde.2023.07.029}},
volume = {{374}},
year = {{2023}},
}
@article{53346,
author = {{Winkler, Michael}},
issn = {{1079-9389}},
journal = {{Advances in Differential Equations}},
keywords = {{Applied Mathematics, Analysis}},
number = {{11/12}},
publisher = {{Khayyam Publishing, Inc}},
title = {{{Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing}}},
doi = {{10.57262/ade028-1112-921}},
volume = {{28}},
year = {{2023}},
}
@article{45984,
author = {{Kaur, Mannat and Sri Ramulu, Harshini and Acar, Yasemin and Fiebig, Tobias}},
journal = {{Proc. ACM Hum. Comput. Interact.}},
number = {{CSCW1}},
pages = {{1–38}},
title = {{{"Oh yes! over-preparing for meetings is my jam :)": The Gendered Experiences of System Administrators}}},
doi = {{10.1145/3579617}},
volume = {{7}},
year = {{2023}},
}
@book{51101,
author = {{Werth, Gerda}},
isbn = {{9783658424442}},
issn = {{2661-8591}},
publisher = {{Springer Fachmedien Wiesbaden}},
title = {{{Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings}}},
doi = {{10.1007/978-3-658-42445-9}},
year = {{2023}},
}
@article{51103,
author = {{Werth, Gerda}},
journal = {{mathematik lehren}},
pages = {{15--19}},
publisher = {{Friedrich}},
title = {{{Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe}}},
volume = {{241}},
year = {{2023}},
}
@inproceedings{51739,
author = {{Weiß, Deborah and Duffe, Tobias and Buczek, Moritz and Kullmer, Gunter and Schramm, Britta}},
location = {{Berlin}},
publisher = {{Deutscher Verband für Materialforschung und -prüfung e.V.}},
title = {{{Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss}}},
doi = {{10.48447/WP-2023-244}},
year = {{2023}},
}
@inbook{35904,
author = {{Böttger, Lydia and Niederhaus, Constanze}},
booktitle = {{Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive}},
editor = {{Efing, Christian and Kalkavan-Aydin, Zeynep}},
publisher = {{De Gruyter}},
title = {{{CLIL - Content and Language Integrated Learning}}},
doi = {{https://doi.org/10.1515/9783110745504}},
year = {{2023}},
}
@unpublished{53404,
abstract = {{In this short note we observe, on locally symmetric spaces of higher rank, a
connection between the growth indicator function introduced by Quint and the
modified critical exponent of the Poincar\'e series equipped with the
polyhedral distance. As a consequence, we provide a different characterization
of the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms
of the growth indicator function. Moreover, we explore the relationship between
these three objects and the temperedness.}},
author = {{Wolf, Lasse L. and Zhang, Hong-Wei}},
booktitle = {{arXiv:2311.11770}},
title = {{{$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces}}},
year = {{2023}},
}
@inbook{53405,
abstract = {{Das Verhältnis zwischen Wissenschaft und Praxis wurde in unterschiedlichen Forschungsansätzen im-
mer wieder wissenschaftlich betrachtet. Dennoch ist es notwendig, sich im Rahmen der wissenschafts-
theoretischen Konzeption von Design-Based Research (DBR) weiter damit auseinanderzusetzen, denn
Interaktion zwischen Wissenschaft und Bildungspraxis ist ein zentrales Merkmal von DBR. Dieser Beitrag
befasst sich mit der Frage, wie sich diese Interaktion je nach zugrunde liegendem DBR-Verständnis me-
thodologisch fassen lässt. Die Interaktion wird als ein wesentlicher Bestandteil des Erkenntnisprozesses
in DBR aufgefasst. Daher wird neben der methodischen Ausgestaltung von Interaktionsprozessen auch
methodologisch reflektiert, was die Wissenschaft-Praxis-Interaktion für die Erkenntnis an sich bedeutet.}},
author = {{Jenert, Tobias}},
booktitle = {{Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung}},
editor = {{Kremer, H.-Hugo and Ertl, Hubert and Sloane, Peter F. E.}},
pages = {{11--24}},
publisher = {{Bundesinstitut für Berufsbildung.}},
title = {{{Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis}}},
year = {{2023}},
}
@inproceedings{52380,
author = {{Sparmann, Sören and Hüsing, Sven and Schulte, Carsten}},
booktitle = {{Proceedings of the 23rd Koli Calling International Conference on Computing Education Research}},
publisher = {{ACM}},
title = {{{JuGaze: A Cell-based Eye Tracking and Logging Tool for Jupyter Notebooks}}},
doi = {{10.1145/3631802.3631824}},
year = {{2023}},
}
@article{53410,
abstract = {{AbstractWe consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.}},
author = {{Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}},
issn = {{1424-0637}},
journal = {{Annales Henri Poincaré}},
keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}},
number = {{2}},
pages = {{1607--1656}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}}},
doi = {{10.1007/s00023-023-01379-x}},
volume = {{25}},
year = {{2023}},
}