A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion - Winkler, Michael (Annales de l'Institut Henri Poincaré C, Analyse non linéaire)
Keywords: Mathematical Physics; Analysis; Applied Mathematics

Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities - Li, Genglin; Winkler, Michael (Applicable Analysis)
Keywords: Applied Mathematics; Analysis

Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers - Tao, Youshan; Winkler, Michael (Mathematical Models and Methods in Applied Sciences)
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.
Keywords: Applied Mathematics; Modeling and Simulation

A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system - Ahn, Jaewook; Winkler, Michael (Calculus of Variations and Partial Differential Equations)
Keywords: Applied Mathematics; Analysis

Analysis of a chemotaxis-SIS epidemic model with unbounded infection force - Tao, Youshan; Winkler, Michael (Nonlinear Analysis: Real World Applications)
Keywords: Applied Mathematics; Computational Mathematics; General Economics; Econometrics and Finance; General Engineering; General Medicine; Analysis

Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities - Li, Genglin; Winkler, Michael (Communications in Mathematical Sciences)
Keywords: Applied Mathematics; General Mathematics

Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type - Winkler, Michael (Open Mathematics)
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) .
Keywords: General Mathematics

Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction - Winkler, Michael (Nonlinearity)
Abstract A no-flux initial-boundary value problem for <?CDATA \begin{align*} \begin{cases} u_t = \Delta \big(u\phi(v)\big), \\[1mm] v_t = \Delta v-uv, \end{cases} \qquad \qquad (\star) \end{align*}?> <mml:mtable columnalign="right left right left right left right left right left right left" columnspacing="0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em" rowspacing="3pt">ut=Δ(uϕ(v)),vt=Δv−uv,(⋆) is considered in smoothly bounded subdomains of <?CDATA $\mathbb{R}^n$?> Rn with <?CDATA $n\geqslant 1$?> n⩾1 and suitably regular initial data, where φ is assumed to reflect algebraic type cross-degeneracies by sharing essential features with <?CDATA $0\leqslant \xi\mapsto \xi^\alpha$?> 0⩽ξ↦ξα for some <?CDATA $\alpha\geqslant 1$?> α⩾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 profile <?CDATA $u_\infty$?> u∞ and some null set <?CDATA $N_\star\subset (0,\infty)$?> N⋆⊂(0,∞) , a corresponding global generalized solution, known to exist according to recent literature, satisfies <?CDATA \begin{align*} \rho(u(\cdot,t))\stackrel{\star}{\rightharpoonup} \rho(u_\infty) \quad \textrm{in } L^\infty(\Omega) \quad\;\; \textrm{ and } \quad\;\; v(\cdot,t)\to 0 \quad \textrm{in } L^p(\Omega)\; \textrm{for all } p\geqslant 1 \end{align*}?> <mml:mtable columnalign="right left right left right left right left right left right left" columnspacing="0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em" rowspacing="3pt">ρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1 as <?CDATA $(0,\infty)\setminus N_\star \ni t\to \infty$?> (0,∞)∖N⋆∋t→∞ , where <?CDATA $\rho(\xi): = \frac{\xi^2}{(\xi+1)^2}$?> ρ(ξ):=ξ2(ξ+1)2 , <?CDATA $\xi\geqslant 0$?> ξ⩾0 . In the particular case when either <?CDATA $n\leqslant 2$?> n⩽2 and <?CDATA $\alpha\geqslant 1$?> α⩾1 is arbitrary, or <?CDATA $n\geqslant 1$?> n⩾1 and <?CDATA $\alpha\in [1,2]$?> α∈[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 <?CDATA $(u_\star,0)$?> (u⋆,0) of ( <?CDATA $\star$?> ⋆ ) is stable with respect to a suitably chosen norm topology.
Keywords: Applied Mathematics; General Physics and Astronomy; Mathematical Physics; Statistical and Nonlinear Physics

Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity - Winkler, Michael (Journal of Elliptic and Parabolic Equations)
Abstract The 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.
Keywords: Applied Mathematics; Numerical Analysis; Analysis

Keller–Segel–Stokes interaction involving signal‐dependent motilities - Tian, Yu; Winkler, Michael (Mathematical Methods in the Applied Sciences)
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.
Keywords: General Engineering; General Mathematics

Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities - Painter, Kevin J.; Winkler, Michael (SIAM Journal on Applied Mathematics)
Keywords: Applied Mathematics

Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems - Winkler, Michael; Yokota, Tomomi (Journal of Differential Equations)
Keywords: Analysis; Applied Mathematics

Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing - Winkler, Michael (Advances in Differential Equations)
Keywords: Applied Mathematics; Analysis

"Oh yes! over-preparing for meetings is my jam :)": The Gendered Experiences of System Administrators - Kaur, Mannat; Sri Ramulu, Harshini; Acar, Yasemin; Fiebig, Tobias (Proc. ACM Hum. Comput. Interact.)

Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings - Werth, Gerda

Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe - Werth, Gerda (mathematik lehren)

Bruchmechanische Untersuchung des Dualphasenstahls HCT590X unter Temperatureinfluss - Weiß, Deborah; Duffe, Tobias; Buczek, Moritz; Kullmer, Gunter; Schramm, Britta

CLIL - Content and Language Integrated Learning - Böttger, Lydia; Niederhaus, Constanze (Berufs- und Fachsprache Deutsch in Wissenschaft und Praxis. Ein Handbuch aus DaF- und DaZ Perspektive)

$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces - Wolf, Lasse L.; Zhang, Hong-Wei (arXiv:2311.11770)
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.

Design-Based Research als Erforschung und Gestaltung von Interaktionsprozessen zwischen Wissenschaft und Bildungspraxis - Jenert, Tobias (Wissenschaft trifft Praxis – Designbasierte Forschung in der beruflichen Bildung)
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.