@article{53262,
author = {{Santamaria, Ignacio and Soleymani, Mohammad and Jorswieck, Eduard and Gutiérrez, Jesús}},
issn = {{1070-9908}},
journal = {{IEEE Signal Processing Letters}},
keywords = {{Applied Mathematics, Electrical and Electronic Engineering, Signal Processing}},
pages = {{923--926}},
publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}},
title = {{{SNR Maximization in Beyond Diagonal RIS-Assisted Single and Multiple Antenna Links}}},
doi = {{10.1109/lsp.2023.3296902}},
volume = {{30}},
year = {{2023}},
}
@article{53261,
author = {{Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard and Clerckx, Bruno}},
issn = {{1536-1276}},
journal = {{IEEE Transactions on Wireless Communications}},
keywords = {{Applied Mathematics, Electrical and Electronic Engineering, Computer Science Applications}},
pages = {{1--1}},
publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}},
title = {{{Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-assisted URLLC Systems}}},
doi = {{10.1109/twc.2023.3324190}},
year = {{2023}},
}
@article{53317,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{2163-2480}},
journal = {{Evolution Equations and Control Theory}},
keywords = {{Applied Mathematics, Control and Optimization, Modeling and Simulation}},
number = {{6}},
pages = {{1676--1687}},
publisher = {{American Institute of Mathematical Sciences (AIMS)}},
title = {{{Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities}}},
doi = {{10.3934/eect.2023031}},
volume = {{12}},
year = {{2023}},
}
@article{53320,
author = {{Winkler, Michael}},
issn = {{0294-1449}},
journal = {{Annales de l'Institut Henri Poincaré C, Analyse non linéaire}},
keywords = {{Mathematical Physics, Analysis, Applied Mathematics}},
publisher = {{European Mathematical Society - EMS - Publishing House GmbH}},
title = {{{A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion}}},
doi = {{10.4171/aihpc/73}},
year = {{2023}},
}
@article{53318,
author = {{Li, Genglin and Winkler, Michael}},
issn = {{0003-6811}},
journal = {{Applicable Analysis}},
keywords = {{Applied Mathematics, Analysis}},
number = {{1}},
pages = {{45--64}},
publisher = {{Informa UK Limited}},
title = {{{Refined regularity analysis for a Keller-Segel-consumption system involving signal-dependent motilities}}},
doi = {{10.1080/00036811.2023.2173183}},
volume = {{103}},
year = {{2023}},
}
@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{53229,
author = {{Santos-Arteaga, Francisco J. and Di Caprio, Debora and Tavana, Madjid and Tena, Emilio Cerda}},
issn = {{1063-6706}},
journal = {{IEEE Transactions on Fuzzy Systems}},
keywords = {{Applied Mathematics, Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering}},
number = {{2}},
pages = {{460--474}},
publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}},
title = {{{A Credibility and Strategic Behavior Approach in Hesitant Multiple Criteria Decision-Making With Application to Sustainable Transportation}}},
doi = {{10.1109/tfuzz.2022.3188875}},
volume = {{31}},
year = {{2023}},
}
@article{53539,
abstract = {{AbstractThe infinite Brownian loop on a Riemannian manifold is the limit in distribution of the Brownian bridge of length T around a fixed origin when $$T \rightarrow +\infty $$
T
→
+
∞
. The aim of this note is to study its long-time asymptotics on Riemannian symmetric spaces G/K of noncompact type and of general rank. This amounts to the behavior of solutions to the heat equation subject to the Doob transform induced by the ground spherical function. Unlike the standard Brownian motion, we observe in this case phenomena which are similar to the Euclidean setting, namely $$L^1$$
L
1
asymptotic convergence without requiring bi-K-invariance for initial data, and strong $$L^{\infty }$$
L
∞
convergence.}},
author = {{Papageorgiou, Efthymia}},
issn = {{2296-9020}},
journal = {{Journal of Elliptic and Parabolic Equations}},
keywords = {{Applied Mathematics, Numerical Analysis, Analysis}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Asymptotics for the infinite Brownian loop on noncompact symmetric spaces}}},
doi = {{10.1007/s41808-023-00250-8}},
year = {{2023}},
}
@article{53538,
abstract = {{AbstractWe study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane.}},
author = {{Polychrou, G. and Papageorgiou, Efthymia and Fotiadis, A. and Daskaloyannis, C.}},
issn = {{1139-1138}},
journal = {{Revista Matemática Complutense}},
keywords = {{General Mathematics}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation}}},
doi = {{10.1007/s13163-023-00476-z}},
year = {{2023}},
}
@article{45786,
abstract = {{Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers.}},
author = {{Hoffmann, Max and Biehler, Rolf}},
issn = {{1863-9690}},
journal = {{ZDM – Mathematics Education}},
keywords = {{General Mathematics, Education}},
publisher = {{Springer}},
title = {{{Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}}},
doi = {{10.1007/s11858-023-01505-3}},
year = {{2023}},
}