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

Analysis of a chemotaxis-SIS epidemic model with unbounded infection force - Tao, Youshan; Winkler, Michael (Nonlinear Analysis: Real World Applications)

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 <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 Rn with n⩾1 and suitably regular initial data, where φ is assumed to reflect algebraic type cross-degeneracies by sharing essential features with 0⩽ξ↦ξα for some 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 u∞ and some null set N⋆⊂(0,∞) , a corresponding global generalized solution, known to exist according to recent literature, satisfies <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 (0,∞)∖N⋆∋t→∞ , where ρ(ξ):=ξ2(ξ+1)2 , ξ⩾0 . In the particular case when either n⩽2 and α⩾1 is arbitrary, or n⩾1 and 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 (u⋆,0) of ( ⋆ ) is stable with respect to a suitably chosen norm topology.

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.

Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities - Tao, Youshan; Winkler, Michael (Evolution Equations and Control Theory)

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

Global generalized solvability in a strongly degenerate taxis-type parabolic system modeling migration–consumption interaction - Winkler, Michael (Zeitschrift für angewandte Mathematik und Physik)
Abstract The parabolic problem $$\begin{aligned} \left\{ \begin{array}{l} u_t=\Delta \big (u\phi (v)\big ), \\ v_t=\Delta v-uv, \end{array} \right. \end{aligned}$$ u t = Δ ( u ϕ ( v ) ) , v t = Δ v - u v , is considered in smoothly bounded subdomains of $${\mathbb {R}}^n$$ R n with arbitrary $$n\ge 1$$ n ≥ 1 . Under the assumptions that $$\phi \in C^0([0,\infty )) \cap C^3((0,\infty ))$$ ϕ ∈ C 0 ( [ 0 , ∞ ) ) ∩ C 3 ( ( 0 , ∞ ) ) is positive on $$(0,\infty )$$ ( 0 , ∞ ) and satisfies $$\begin{aligned} \liminf _{\xi \searrow 0} \frac{\phi (\xi )}{\xi ^\alpha }>0 \quad {\text{ and }} \quad \limsup _{\xi \searrow 0} \big \{ \xi ^\beta |\phi '(\xi )| \big \}<\infty \end{aligned}$$ lim inf ξ ↘ 0 ϕ ( ξ ) ξ α > 0 and lim sup ξ ↘ 0 { ξ β | ϕ ′ ( ξ ) | } < ∞ with some $$\alpha >0$$ α > 0 and $$\beta >0$$ β > 0 , for all reasonably regular initial data an associated no-flux type initial-boundary value problem is shown to admit a global solution in an appropriately generalized sense. This extends previously developed solution theories on problems of this form, which either concentrated on non-degenerate or weakly degenerate cases corresponding to the choices $$\alpha =0$$ α = 0 and $$\alpha \in (0,2)$$ α ∈ ( 0 , 2 ) , or were restricted to low-dimensional settings by requiring that $$n\le 2$$ n ≤ 2 .

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

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)
The taxis-type migration–consumption model accounting for signal-dependent motilities, as given by u_{t} = \Delta (u\phi(v)) , v_{t} = \Delta v-uv , is considered for suitably smooth functions \phi\colon[0,\infty)\to\R which are such that \phi>0 on (0,\infty) , but that in addition \phi(0)=0 with \phi'(0)>0 . In order to appropriately cope with the diffusion degeneracies thereby included, this study separately examines the Neumann problem for the linear equation V_{t} = \Delta V + \nabla\cdot ( a(x,t)V) + b(x,t)V and establishes a statement on how pointwise positive lower bounds for nonnegative solutions depend on the supremum and the mass of the initial data, and on integrability features of a and b . This is thereafter used as a key tool in the derivation of a result on global existence of solutions to the equation above, smooth and classical for positive times, under the mere assumption that the suitably regular initial data be nonnegative in both components. Apart from that, these solutions are seen to stabilize toward some equilibrium, and as a qualitative effect genuinely due to degeneracy in diffusion, a criterion on initial smallness of the second component is identified as sufficient for this limit state to be spatially nonconstant.

Depleting the signal: Analysis of chemotaxis‐consumption models—A survey - Lankeit, Johannes; Winkler, Michael (Studies in Applied Mathematics)
Abstract We give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis‐consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures.
Keywords: Applied Mathematics

Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $\R^n$ - Colasuonno, Francesca; Winkler, Michael (ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)

Finite-Set Direct Torque Control via Edge Computing-Assisted Safe Reinforcement Learning for a Permanent Magnet Synchronous Motor - Schenke, Maximilian; Haucke-Korber, Barnabas; Wallscheid, Oliver (IEEE Transactions on Power Electronics)
Keywords: Electrical and Electronic Engineering

Deep Q Direct Torque Control with a Reduced Control Set Towards Six-Step Operation of Permanent Magnet Synchronous Motors - Haucke-Korber, Barnabas; Schenke, Maximilian; Wallscheid, Oliver (2023 IEEE International Electric Machines & Drives Conference (IEMDC))

Gym-Electric-Motor (GEM) Control: An Automated Open-Source Controller Design Suite for Drives - Book, Felix; Traue, Arne; Schenke, Maximilian; Haucke-Korber, Barnabas; Wallscheid, Oliver (2023 IEEE International Electric Machines & Drives Conference (IEMDC))

Attention to diversity in German CLIL classrooms: Multi-perspective research on students’ and teachers’ perceptions - Siepmann, Philipp; Rumlich, Dominik; Matz, Frauke; Römhild, Ricardo (International Journal of Bilingual Education and Bilingualism)

Inverse procedure for measuring piezoelectric material parameters using a single multi-electrode sample - Claes, Leander; Feldmann, Nadine; Schulze, Veronika; Meihost, Lars; Kuhlmann, Henrik; Jurgelucks, Benjamin; Walther, Andrea; Henning, Bernd (Journal of Sensors and Sensor Systems)

Inverse procedure for the identification of piezoelectric material parameters supported by dense neural networks - Claes, Leander; Meihost, Lars; Jurgelucks, Benjamin

Parameter Identification of Piezoelectrics improved by Neural Networks - Jurgelucks, Benjamin

Parameter identification in piezoelectricity based on all-at-once and reduced regularization - Kuess, Raphael

Investigating Speaker Embedding Disentanglement on Natural Read Speech - Kuhlmann, Michael; Meise, Adrian Tobias; Seebauer, Fritz; Wagner, Petra; Häb-Umbach, Reinhold (Speech Communication; 15th ITG Conference)