@article{63213,
abstract = {{Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: Perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually unbiased bases (MUBs). Uncertainty relations derived from joint properties of the MUBs are generally assumed to be uniform, irrespective of the specific observables chosen within a set. In this work, we demonstrate instead that the uncertainty relations can depend on the choice of observables. Through both experimental observation and numerical methods, we show that selecting different sets of three MUBs in a five-dimensional quantum system results in distinct uncertainty bounds, i.e., in varying degrees of complementarity, in terms of both entropy and variance.}},
author = {{Serino, Laura Maria and Chesi, Giovanni and Brecht, Benjamin and Maccone, Lorenzo and Macchiavello, Chiara and Silberhorn, Christine}},
issn = {{2643-1564}},
journal = {{Physical Review Research}},
number = {{3}},
publisher = {{American Physical Society (APS)}},
title = {{{Complementarity-based complementarity: The choice of mutually unbiased observables shapes quantum uncertainty relations}}},
doi = {{10.1103/v24q-sl6n}},
volume = {{7}},
year = {{2025}},
}
@inbook{63212,
author = {{Riese, Josef and Reinhold, Peter}},
booktitle = {{Handbuch Lehrerinnen- und Lehrerbildung}},
editor = {{Cramer, Colin and König, Johannes and Rothland, Martin}},
isbn = {{978-3-8365-6544-6}},
publisher = {{Verlag Julius Klinkhardt}},
title = {{{Physik in der Lehrerinnen- und Lehrerbildung - Empirisch fundierte Curricula in einer digitalen Welt}}},
doi = {{10.35468/hblb2025-076}},
year = {{2025}},
}
@unpublished{63187,
author = {{Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}},
booktitle = {{arXiv:2512.14285}},
title = {{{Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor}}},
year = {{2025}},
}
@article{63214,
abstract = {{We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale.}},
author = {{Horoshko, Dmitri B. and Srivastava, Shivang and Sośnicki, Filip and Mikołajczyk, Michał and Karpiński, Michał and Brecht, Benjamin and Kolobov, Mikhail I.}},
issn = {{2469-9926}},
journal = {{Physical Review A}},
number = {{2}},
publisher = {{American Physical Society (APS)}},
title = {{{Time-resolved second-order autocorrelation function of parametric down-conversion}}},
doi = {{10.1103/7ckm-tm3r}},
volume = {{112}},
year = {{2025}},
}
@article{63215,
abstract = {{Abstract
High-dimensional time-frequency encodings have the potential to significantly advance quantum information science; however, practical applications require precise knowledge of the encoded quantum states, which becomes increasingly challenging for larger Hilbert spaces. Self-guided tomography (SGT) has emerged as a practical and scalable technique for this purpose in the spatial domain. Here, we apply SGT to estimate time-frequency states using a multi-output quantum pulse gate. We achieve fidelities of more than 99% for 3- and 5-dimensional states without the need for calibration or post-processing. We demonstrate the robustness of SGT against statistical and environmental noise, highlighting its efficacy in the photon-starved regime typical of quantum information applications.}},
author = {{Serino, Laura Maria and Rambach, Markus and Brecht, Benjamin and Romero, Jacquiline and Silberhorn, Christine}},
issn = {{2058-9565}},
journal = {{Quantum Science and Technology}},
number = {{2}},
publisher = {{IOP Publishing}},
title = {{{Self-guided tomography of time-frequency qudits}}},
doi = {{10.1088/2058-9565/adb0ea}},
volume = {{10}},
year = {{2025}},
}
@article{63223,
abstract = {{AbstractThe quartz crystal microbalance with dissipation monitoring (QCM‐D) is routinely used to investigate structured samples. Here, a simulation technique is described, that predicts the shifts of frequency and half bandwidth, Δfn and ΔΓn, of a quartz resonator operating on different overtone orders, n, induced by structured samples in contact with the resonator surface in liquid. The technique, abbreviated as FreqD‐LBM, solves the Stokes equation in the frequency domain. The solution provides the complex amplitude of the area‐averaged tangential stress at the resonator surface, from which Δfn and ΔΓn are derived. Because the dynamical variables are complex amplitudes, the viscosity can be complex, as well. The technique naturally covers viscoelasticity. Limitations are linked to the grid resolution and to problems at large viscosity. Validation steps include viscoelastic films, rough surfaces, an oscillating cylinder in a viscous medium, and a free‐floating sphere above the resonator. Application examples are soft adsorbed particles, stiff adsorbed particles, and a large, immobile spherical cap above the resonator, which allows to study the high‐frequency properties of the material in the gap. FreqDLBM runs on an office PC and does not require expert knowledge of numerical techniques. It is accessible to an experimentalist.}},
author = {{Johannsmann, Diethelm and Häusner, Paul and Langhoff, Arne and Leppin, Christian and Reviakine, Ilya and Vanoppen, Viktor}},
issn = {{2513-0390}},
journal = {{Advanced Theory and Simulations}},
number = {{7}},
publisher = {{Wiley}},
title = {{{The Frequency‐Domain Lattice Boltzmann Method (FreqD‐LBM): A Versatile Tool to Predict the QCM Response Induced by Structured Samples}}},
doi = {{10.1002/adts.202401373}},
volume = {{8}},
year = {{2025}},
}
@article{63222,
abstract = {{The solid electrolyte interphase (SEI) on the anode of lithium-ion batteries (LIBs) has been studied thoroughly due to its crucial importance to the battery’s long-term performance. At the same time, most studies of the SEI apply ex situ characterization methods, which may introduce artifacts or misinterpretations as they do not investigate the SEI in its unaltered state immersed in liquid battery electrolyte. Thus, in this work, we focus on using the non-destructive combination of electrochemical quartz crystal microbalance with dissipation monitoring (EQCM-D) and impedance spectroscopy (EIS) in the same electrochemical cell. EQCM-D can not only probe the solidified products of the SEI but also allows for the monitoring of viscoelastic layers and viscosity changes of the electrolyte at the interphase during the SEI formation. EIS complements those results by providing electrochemical properties of the formed interphase. Our results highlight substantial differences in the physical and electrochemical properties between the SEI formed on copper and on amorphous carbon and show how formation parameters and the additive vinylene carbonate (VC) influence their growth. The EQCM-D results show consistently that much thicker SEIs are formed on carbon substrates in comparison to copper substrates.}},
author = {{Stich, Michael and Leppin, Christian and Krauss, Falk Thorsten and Valdes Landa, Jesus Eduardo and Pantenburg, Isabel and Roling, Bernhard and Bund, Andreas}},
issn = {{2313-0105}},
journal = {{Batteries}},
number = {{7}},
publisher = {{MDPI AG}},
title = {{{Comparing the SEI Formation on Copper and Amorphous Carbon: A Study with Combined Operando Methods}}},
doi = {{10.3390/batteries11070273}},
volume = {{11}},
year = {{2025}},
}
@article{63224,
abstract = {{By monitoring the solidification of droplets of plant latices with a fast quartz crystal microbalance with dissipation monitoring (QCM-D), droplets from Campanula glomerata were found to solidify much faster than droplets from Euphorbia characias and also faster than droplets from all technical latices tested. A similar conclusion was drawn from optical videos, where the plants were injured and the milky fluid was stretched (sometimes forming fibers) after the cut. Rapid solidification cannot be explained with physical drying because physical drying is transport-limited and therefore is inherently slow. It can, however, be explained with coagulation being triggered by a sudden decrease in hydrostatic pressure. A mechanism based on a pressure drop is corroborated by optical videos of both plants being injured under water. While the liquid exuded by E. characias keeps streaming away, the liquid exuded by C. glomerata quickly forms a plug even under water. Presumably, the pressure drop causes an influx of serum into the laticifers. The serum, in turn, triggers a transition from a liquid–liquid phase separated state (an LLPS state) of a resin and hardener to a single-phase state. QCM measurements, optical videos, and cryo-SEM images suggest that LLPS plays a role in the solidification of C. glomerata.}},
author = {{Langhoff, Arne and Peschel, Astrid and Leppin, Christian and Kruppert, Sebastian and Speck, Thomas and Johannsmann, Diethelm}},
issn = {{2223-7747}},
journal = {{Plants}},
number = {{5}},
publisher = {{MDPI AG}},
title = {{{Rapid Solidification of Plant Latices from Campanula glomerata Driven by a Sudden Decrease in Hydrostatic Pressure}}},
doi = {{10.3390/plants14050798}},
volume = {{14}},
year = {{2025}},
}
@article{63225,
abstract = {{Various polycations and polyanions were sequentially adsorbed onto the gold electrode of a quartz crystal microbalance with dissipation monitoring. The study focused on determining the adsorption kinetics, viscoelastic properties, and electroresponsivity of polyelectrolyte layers. For the first time, it was demonstrated that the structure (compact or expanded) of the layers can be determined by electroresponsivity. Viscoelastic modeling alone did not provide a conclusive answer as to whether the layers were compact or expanded. The study was further enriched by streaming potential and contact angle measurements, where polyelectrolyte multilayers were formed on mica. It was found that successive adsorption of layers led to periodic inversion of the zeta potential. Systematic differences were observed between the different top layers, which were explained by intermixing between layers. The presence or absence of interpenetration, as determined by the measurements of streaming potential and contact angles, correlated well with electroresponsivity.}},
author = {{Leppin, Christian and Pomorska, Agata and Morga, Maria and Pomastowski, Pawel and Fijałkowski, Piotr and Michna, Aneta and Johannsmann, Diethelm}},
issn = {{1525-7797}},
journal = {{Biomacromolecules}},
number = {{2}},
pages = {{914--928}},
publisher = {{American Chemical Society (ACS)}},
title = {{{Swelling Degree of Polyelectrolyte Layers Determined by an Electrochemical Quartz Crystal Microbalance}}},
doi = {{10.1021/acs.biomac.4c01205}},
volume = {{26}},
year = {{2025}},
}
@article{63226,
abstract = {{Nanobubbles in water splitting are recognized by the EQCM-D. They are ubiquitous. Lifetimes are in the range of seconds.}},
author = {{Leppin, Christian and Langhoff, Arne and Johannsmann, Diethelm}},
issn = {{1463-9076}},
journal = {{Physical Chemistry Chemical Physics}},
number = {{37}},
pages = {{19733--19747}},
publisher = {{Royal Society of Chemistry (RSC)}},
title = {{{A fast electrochemical quartz crystal microbalance (EQCM) evidences the presence of nanobubbles in alkaline water splitting}}},
doi = {{10.1039/d5cp02691a}},
volume = {{27}},
year = {{2025}},
}
@article{63241,
author = {{Schmitt-Richter, Lena Katharina and Wüllner, Sabrina and Schmidt, Katharina and Ebeling, Muna}},
journal = {{Pädagogikunterricht. Die Fachzeitschrift für die pädagogische Fächergruppe.}},
number = {{4}},
pages = {{65--70}},
title = {{{Von der Idee zur Umsetzung – Der Schulversuch an der Maria-Montessori-Gesamtschule in Düsseldorf}}},
volume = {{45}},
year = {{2025}},
}
@article{63250,
abstract = {{Abstract
An initial-boundary value problem for
$$\begin{aligned} \left\{ \begin{array}{ll}u_{tt} = \big (\gamma (\Theta ) u_{xt}\big )_x + au_{xx} - \big (f(\Theta )\big )_x, \qquad & x\in \Omega , \ t>0, \\[1mm] \Theta _t = \Theta _{xx} + \gamma (\Theta ) u_{xt}^2 - f(\Theta ) u_{xt}, \qquad & x\in \Omega , \ t>0, \end{array} \right. \end{aligned}$$
u
tt
=
(
γ
(
Θ
)
u
xt
)
x
+
a
u
xx
-
(
f
(
Θ
)
)
x
,
x
∈
Ω
,
t
>
0
,
[
1
m
m
]
Θ
t
=
Θ
xx
+
γ
(
Θ
)
u
xt
2
-
f
(
Θ
)
u
xt
,
x
∈
Ω
,
t
>
0
,
is considered in an open bounded real interval
$$\Omega $$
Ω
. Under the assumption that
$$\gamma \in C^0([0,\infty ))$$
γ
∈
C
0
(
[
0
,
∞
)
)
and
$$f\in C^0([0,\infty ))$$
f
∈
C
0
(
[
0
,
∞
)
)
are such that
$$f(0)=0$$
f
(
0
)
=
0
, and
$$k_\gamma \le \gamma \le K_\gamma $$
k
γ
≤
γ
≤
K
γ
as well as
$$\begin{aligned} |f(\xi )| \le K_f \cdot (\xi +1)^\alpha \qquad \hbox {for all } \xi \ge 0 \end{aligned}$$
|
f
(
ξ
)
|
≤
K
f
·
(
ξ
+
1
)
α
for all
ξ
≥
0
with some
$$k_\gamma>0, K_\gamma>0, K_f>0$$
k
γ
>
0
,
K
γ
>
0
,
K
f
>
0
and
$$\alpha <\frac{3}{2}$$
α
<
3
2
, for all suitably regular initial data of arbitrary size a statement on global existence of a global weak solution is derived. By particularly covering the thermodynamically consistent choice
$$f\equiv id$$
f
≡
i
d
of predominant physical relevance, this appears to go beyond previous related literature which seems to either rely on independence of
$$\gamma $$
γ
on
$$\Theta $$
Θ
, or to operate on finite time intervals.
}},
author = {{Winkler, Michael}},
issn = {{0044-2275}},
journal = {{Zeitschrift für angewandte Mathematik und Physik}},
number = {{5}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities}}},
doi = {{10.1007/s00033-025-02582-y}},
volume = {{76}},
year = {{2025}},
}
@article{63249,
abstract = {{Abstract
The model
$$\begin{aligned} \left\{ \begin{array}{l}u_{tt} = \big (\gamma (\Theta ) u_{xt}\big )_x + au_{xx} - \big (f(\Theta )\big )_x, \\[1mm] \Theta _t = \Theta _{xx} + \gamma (\Theta ) u_{xt}^2 - f(\Theta ) u_{xt}, \end{array} \right. \end{aligned}$$
u
tt
=
(
γ
(
Θ
)
u
xt
)
x
+
a
u
xx
-
(
f
(
Θ
)
)
x
,
[
1
m
m
]
Θ
t
=
Θ
xx
+
γ
(
Θ
)
u
xt
2
-
f
(
Θ
)
u
xt
,
for thermoviscoelastic evolution in one-dimensional Kelvin–Voigt materials is considered. By means of an approach based on maximal Sobolev regularity theory of scalar parabolic equations, it is shown that if
$$\gamma _0>0$$
γ
0
>
0
is fixed, then there exists
$$\delta =\delta (\gamma _0)>0$$
δ
=
δ
(
γ
0
)
>
0
with the property that for suitably regular initial data of arbitrary size an associated initial boundary value problem posed in an open bounded interval admits a global classical solution whenever
$$\gamma \in C^2([0,\infty ))$$
γ
∈
C
2
(
[
0
,
∞
)
)
and
$$f\in C^2([0,\infty ))$$
f
∈
C
2
(
[
0
,
∞
)
)
are such that
$$f(0)=0$$
f
(
0
)
=
0
and
$$|f(\xi )| \le K_f \cdot (\xi +1)^\alpha $$
|
f
(
ξ
)
|
≤
K
f
·
(
ξ
+
1
)
α
for all
$$\xi \ge 0$$
ξ
≥
0
and some
$$K_f>0$$
K
f
>
0
and
$$\alpha <\frac{3}{2}$$
α
<
3
2
, and that
$$\begin{aligned} \gamma _0 \le \gamma (\xi ) \le \gamma _0 + \delta \qquad \hbox {for all } \xi \ge 0. \end{aligned}$$
γ
0
≤
γ
(
ξ
)
≤
γ
0
+
δ
for all
ξ
≥
0
.
This is supplemented by a statement on global existence of certain strong solutions, particularly continuous in both components, under weaker conditions on the initial data.
}},
author = {{Winkler, Michael}},
issn = {{1424-3199}},
journal = {{Journal of Evolution Equations}},
number = {{4}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities}}},
doi = {{10.1007/s00028-025-01144-z}},
volume = {{25}},
year = {{2025}},
}
@article{63246,
abstract = {{Abstract
The hyperbolic-parabolic model
$$\begin{aligned} \left\{ \begin{array}{ll} u_{tt} = u_{xx} - \big (f(\Theta )\big )_x, \qquad & x\in \Omega , \ t>0, \\ \Theta _t = \Theta _{xx} - f(\Theta ) u_{xt}, \qquad & x\in \Omega , \ t>0, \end{array} \right. \end{aligned}$$
u
tt
=
u
xx
-
(
f
(
Θ
)
)
x
,
x
∈
Ω
,
t
>
0
,
Θ
t
=
Θ
xx
-
f
(
Θ
)
u
xt
,
x
∈
Ω
,
t
>
0
,
for the evolution of the displacement variable
u
and the temperature
$$\Theta \ge 0$$
Θ
≥
0
during thermoelastic interaction in a one-dimensional bounded interval
$$\Omega $$
Ω
is considered. Whereas the literature has provided comprehensive results on global solutions for sufficiently regular initial data
$$(u_0,u_{0t},\Theta _0)=(u,u_t,\Theta )|_{t=0}$$
(
u
0
,
u
0
t
,
Θ
0
)
=
(
u
,
u
t
,
Θ
)
|
t
=
0
when
$$f\equiv id$$
f
≡
i
d
, it seems to have remained open so far how far a solution theory can be built solely on the two fundamental physical principles of energy conservation and entropy nondecrease. The present manuscript addresses this by asserting global existence of weak solutions under assumptions which are energy- and entropy-minimal in the sense of allowing for any initial data
$$u_0\in W_0^{1,2}(\Omega )$$
u
0
∈
W
0
1
,
2
(
Ω
)
,
$$u_{0t} \in L^2(\Omega )$$
u
0
t
∈
L
2
(
Ω
)
and
$$0\le \Theta _0\in L^1(\Omega )$$
0
≤
Θ
0
∈
L
1
(
Ω
)
, and which apply to arbitrary
$$f\in C^1([0,\infty ))$$
f
∈
C
1
(
[
0
,
∞
)
)
with
$$f(0)=0$$
f
(
0
)
=
0
and
$$f'>0$$
f
′
>
0
on
$$[0,\infty )$$
[
0
,
∞
)
.
}},
author = {{Winkler, Michael}},
issn = {{0944-2669}},
journal = {{Calculus of Variations and Partial Differential Equations}},
number = {{1}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Rough solutions in one-dimensional nonlinear thermoelasticity}}},
doi = {{10.1007/s00526-025-03170-8}},
volume = {{65}},
year = {{2025}},
}
@article{63244,
abstract = {{
The Cauchy problem in
\mathbb{R}^{n}
for the cross-diffusion system
\begin{cases}u_{t} = \nabla \cdot (D(u)\nabla u) - \nabla\cdot (u\nabla v), \\ 0 = \Delta v +u,\end{cases}
is considered for
n\ge 2
and under assumptions ensuring that
D
suitably generalizes the prototype given by
D(\xi)=(\xi+1)^{-\alpha}, \quad \xi\ge 0.
Under the assumption that
\alpha>1
, it is shown that for any
r_{\star}>0
and
\delta\in (0,1)
one can find radially symmetric initial data from
C_{0}^{\infty}(\mathbb{R}^{n})
such that the corresponding solution blows up within some finite time, and that this explosion occurs throughout certain spheres in an appropriate sense, with any such sphere being located in the annulus
\overline{B}_{r_\star+\delta}(0)\setminus B_{(1-\delta)r_\star}(0)
.This is complemented by a result revealing that when
\alpha<1
, any finite-mass unbounded radial solution must blow up exclusively at the spatial origin.
}},
author = {{Winkler, Michael}},
issn = {{1435-9855}},
journal = {{Journal of the European Mathematical Society}},
publisher = {{European Mathematical Society - EMS - Publishing House GmbH}},
title = {{{Can diffusion degeneracies enhance complexity in chemotactic aggregation? Finite-time blow-up on spheres in a quasilinear Keller–Segel system}}},
doi = {{10.4171/jems/1607}},
year = {{2025}},
}
@article{63247,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
pages = {{197--239}},
publisher = {{Elsevier BV}},
title = {{{A switch in dimension dependence of critical blow-up exponents in a Keller-Segel system involving indirect signal production}}},
doi = {{10.1016/j.jde.2024.12.040}},
volume = {{423}},
year = {{2025}},
}
@article{63252,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{1674-7283}},
journal = {{Science China Mathematics}},
number = {{12}},
pages = {{2867--2900}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{A unified approach to existence theories for singular chemotaxis systems with nonlinear signal production}}},
doi = {{10.1007/s11425-023-2397-y}},
volume = {{68}},
year = {{2025}},
}
@article{63344,
abstract = {{Abstract
A Neumann-type initial-boundary value problem for
$$\begin{aligned} \left\{ \begin{array}{l} u_{tt} = \nabla \cdot (\gamma (\Theta ) \nabla u_t) + a \nabla \cdot (\gamma (\Theta ) \nabla u) + \nabla \cdot f(\Theta ), \\ \Theta _t = D\Delta \Theta + \Gamma (\Theta ) |\nabla u_t|^2 + F(\Theta )\cdot \nabla u_t, \end{array} \right. \end{aligned}$$
u
tt
=
∇
·
(
γ
(
Θ
)
∇
u
t
)
+
a
∇
·
(
γ
(
Θ
)
∇
u
)
+
∇
·
f
(
Θ
)
,
Θ
t
=
D
Δ
Θ
+
Γ
(
Θ
)
|
∇
u
t
|
2
+
F
(
Θ
)
·
∇
u
t
,
is considered in a smoothly bounded domain
$$\Omega \subset \mathbb {R}^n$$
Ω
⊂
R
n
,
$$n\ge 1$$
n
≥
1
. In the case when
$$n=1$$
n
=
1
,
$$\gamma \equiv \Gamma $$
γ
≡
Γ
and
$$f\equiv F$$
f
≡
F
, this system coincides with the standard model for heat generation in a viscoelastic material of Kelvin-Voigt type, well-understood in situations in which
$$\gamma =const$$
γ
=
c
o
n
s
t
. Covering scenarios in which all key ingredients
$$\gamma ,\Gamma ,f$$
γ
,
Γ
,
f
and F may depend on the temperature
$$\Theta $$
Θ
here, for initial data which merely satisfy
$$u_0\in W^{1,p+2}(\Omega )$$
u
0
∈
W
1
,
p
+
2
(
Ω
)
,
$$u_{0t}\in W^{1,p}(\Omega )$$
u
0
t
∈
W
1
,
p
(
Ω
)
and
$$\Theta _0\in W^{1,p}(\Omega )$$
Θ
0
∈
W
1
,
p
(
Ω
)
with some
$$p\ge 2$$
p
≥
2
such that
$$p>n$$
p
>
n
, a result on local-in-time existence and uniqueness is derived in a natural framework of weak solvability.}},
author = {{Winkler, Michael}},
issn = {{0095-4616}},
journal = {{Applied Mathematics & Optimization}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}}},
doi = {{10.1007/s00245-025-10243-9}},
volume = {{91}},
year = {{2025}},
}
@article{63242,
abstract = {{Abstract
For
$$p>2$$
p
>
2
, the equation
$$\begin{aligned} u_t = u^p u_{xx}, \qquad x\in \mathbb {R}, \ t\in \mathbb {R}, \end{aligned}$$
u
t
=
u
p
u
xx
,
x
∈
R
,
t
∈
R
,
is shown to admit positive and spatially increasing smooth solutions on all of
$$\mathbb {R}\times \mathbb {R}$$
R
×
R
which are precisely of the form of an accelerating wave for
$$t<0$$
t
<
0
, and of a wave slowing down for
$$t>0$$
t
>
0
. These solutions satisfy
$$u(\cdot ,t)\rightarrow 0$$
u
(
·
,
t
)
→
0
in
$$L^\infty _{loc}(\mathbb {R})$$
L
loc
∞
(
R
)
as
$$t\rightarrow + \infty $$
t
→
+
∞
and as
$$t\rightarrow -\infty $$
t
→
-
∞
, and exhibit a yet apparently undiscovered phenomenon of transient rapid spatial growth, in the sense that
$$\begin{aligned} \lim _{x\rightarrow +\infty } x^{-1} u(x,t) \quad \text{ exists } \text{ for } \text{ all } t<0, \end{aligned}$$
lim
x
→
+
∞
x
-
1
u
(
x
,
t
)
exists
for
all
t
<
0
,
that
$$\begin{aligned} \lim _{x\rightarrow +\infty } x^{-\frac{2}{p}} u(x,t) \quad \text{ exists } \text{ for } \text{ all } t>0, \end{aligned}$$
lim
x
→
+
∞
x
-
2
p
u
(
x
,
t
)
exists
for
all
t
>
0
,
but that
$$\begin{aligned} u(x,0)=K e^{\alpha x} \qquad \text{ for } \text{ all } x\in \mathbb {R}\end{aligned}$$
u
(
x
,
0
)
=
K
e
α
x
for
all
x
∈
R
with some
$$K>0$$
K
>
0
and
$$\alpha >0$$
α
>
0
.
}},
author = {{Hanfland, Celina and Winkler, Michael}},
issn = {{2296-9020}},
journal = {{Journal of Elliptic and Parabolic Equations}},
number = {{3}},
pages = {{2041--2063}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Exactly wave-type homoclinic orbits and emergence of transient exponential growth in a super-fast diffusion equation}}},
doi = {{10.1007/s41808-025-00316-9}},
volume = {{11}},
year = {{2025}},
}
@article{63164,
abstract = {{ Refined investigation of chemotaxis processes has revealed a significant role of degeneracies in corresponding motilities in a number of application contexts. A rapidly growing literature concerned with the analysis of resulting mathematical models has been capable of solving fundamental issues, but various problems have remained open, or even newly arisen. The goal of the paper consists in a summary of some developments in this area, and particularly in the discussion of the question how far the introduction of degeneracies may influence the behavior of solutions to chemotaxis systems. }},
author = {{Winkler, Michael}},
issn = {{0218-2025}},
journal = {{Mathematical Models and Methods in Applied Sciences}},
number = {{02}},
pages = {{283--343}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Effects of degeneracies in taxis-driven evolution}}},
doi = {{10.1142/s0218202525400020}},
volume = {{35}},
year = {{2025}},
}