@article{63371,
abstract = {{Adhesion between cells and other cells (cell–cell adhesion) or other tissue components (cell–matrix adhesion) is an intrinsically non-local phenomenon. Consequently, a number of recently developed mathematical models for cell adhesion have taken the form of non-local partial differential equations, where the non-local term arises inside a spatial derivative. The mathematical properties of such a non-local gradient term are not yet well understood. Here we use sophisticated estimation techniques to show local and global existence of classical solutions for such examples of adhesion-type models, and we provide a uniform upper bound for the solutions. Further, we discuss the significance of these results to applications in cell sorting and in cancer invasion and support the theoretical results through numerical simulations.}},
author = {{HILLEN, T. and PAINTER, K. J. and Winkler, Michael}},
issn = {{0956-7925}},
journal = {{European Journal of Applied Mathematics}},
number = {{4}},
pages = {{645--684}},
publisher = {{Cambridge University Press (CUP)}},
title = {{{Global solvability and explicit bounds for non-local adhesion models}}},
doi = {{10.1017/s0956792517000328}},
volume = {{29}},
year = {{2017}},
}
@article{63372,
author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}},
issn = {{0025-5874}},
journal = {{Mathematische Zeitschrift}},
number = {{1-2}},
pages = {{71--108}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system}}},
doi = {{10.1007/s00209-017-1944-6}},
volume = {{289}},
year = {{2017}},
}
@article{63374,
author = {{Winkler, Michael}},
issn = {{0021-7824}},
journal = {{Journal de Mathématiques Pures et Appliquées}},
pages = {{118--169}},
publisher = {{Elsevier BV}},
title = {{{Singular structure formation in a degenerate haptotaxis model involving myopic diffusion}}},
doi = {{10.1016/j.matpur.2017.11.002}},
volume = {{112}},
year = {{2017}},
}
@article{63378,
author = {{Winkler, Michael}},
issn = {{1040-7294}},
journal = {{Journal of Dynamics and Differential Equations}},
number = {{1}},
pages = {{331--358}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{One-Dimensional Super-Fast Diffusion: Persistence Versus Extinction Revisited—Extinction at Spatial Infinity}}},
doi = {{10.1007/s10884-017-9577-3}},
volume = {{30}},
year = {{2017}},
}
@article{63379,
author = {{Winkler, Michael}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
number = {{3}},
pages = {{2310--2350}},
publisher = {{Elsevier BV}},
title = {{{Renormalized radial large-data solutions to the higher-dimensional Keller–Segel system with singular sensitivity and signal absorption}}},
doi = {{10.1016/j.jde.2017.10.029}},
volume = {{264}},
year = {{2017}},
}
@article{63383,
abstract = {{This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by
(\star)
{
u
t
=
∇
⋅
(
u
∇
u
u
2
+
|
∇
u
|
2
)
−
χ
∇
⋅
(
u
∇
v
1
+
|
∇
v
|
2
)
,
0
=
Δ
v
−
μ
+
u
,
\begin{equation}\tag {\star } \begin {cases} u_t=\nabla \cdot \Big (\frac {u\nabla u}{\sqrt {u^2+|\nabla u|^2}}\Big ) - \chi \, \nabla \cdot \Big (\frac {u\nabla v}{\sqrt {1+|\nabla v|^2}}\Big ), \\[3pt] 0=\Delta v - \mu + u, \end{cases} \end{equation}
under the initial condition
u
|
t
=
0
=
u
0
>
0
u|_{t=0}=u_0>0
and no-flux boundary conditions in a ball
Ω
⊂
R
n
\Omega \subset \mathbb {R}^n
, where
χ
>
0
\chi >0
and
μ
:=
1
|
Ω
|
∫
Ω
u
0
\mu :=\frac {1}{|\Omega |} \int _\Omega u_0
. A previous result of the authors [Comm. Partial Differential Equations 42 (2017), 436–473] has asserted global existence of bounded classical solutions for arbitrary positive radial initial data
u
0
∈
C
3
(
Ω
¯
)
u_0\in C^3(\bar \Omega )
when either
n
≥
2
n\ge 2
and
χ
>
1
\chi >1
, or
n
=
1
n=1
and
∫
Ω
u
0
>
1
(
χ
2
−
1
)
+
\int _\Omega u_0>\frac {1}{\sqrt {(\chi ^2-1)_+}}
.
This present paper shows that these conditions are essentially optimal: Indeed, it is shown that if the taxis coefficient satisfies
χ
>
1
\chi >1
, then for any choice of
\[
{
m
>
1
χ
2
−
1
a
m
p
;
if
n
=
1
,
m
>
0
is arbitrary
a
m
p
;
if
n
≥
2
,
\begin {cases} m>\frac {1}{\sqrt {\chi ^2-1}} & \text {if $n=1$}, \\ \text {$m>0$ is arbitrary} & \text {if $n\ge 2$}, \end {cases}
\]
there exist positive initial data
u
0
∈
C
3
(
Ω
¯
)
u_0\in C^3(\bar \Omega )
satisfying
∫
Ω
u
0
=
m
\int _\Omega u_0=m
which are such that for some
T
>
0
T>0
, (
⋆
\star
) possesses a uniquely determined classical solution
(
u
,
v
)
(u,v)
in
Ω
×
(
0
,
T
)
\Omega \times (0,T)
blowing up at time
T
T
in the sense that
lim sup
t
↗
T
‖
u
(
⋅
,
t
)
‖
L
∞
(
Ω
)
=
∞
\limsup _{t\nearrow T} \|u(\cdot ,t)\|_{L^\infty (\Omega )}=\infty
.
This result is derived by means of a comparison argument applied to the doubly degenerate scalar parabolic equation satisfied by the mass accumulation function associated with (
⋆
\star
).
}},
author = {{Bellomo, Nicola and Winkler, Michael}},
issn = {{2330-0000}},
journal = {{Transactions of the American Mathematical Society, Series B}},
number = {{2}},
pages = {{31--67}},
publisher = {{American Mathematical Society (AMS)}},
title = {{{Finite-time blow-up in a degenerate chemotaxis system with flux limitation}}},
doi = {{10.1090/btran/17}},
volume = {{4}},
year = {{2017}},
}
@article{63040,
author = {{Thevenard, L. and Boutigny, B. and Güsken, Nicholas Alexander and Becerra, L. and Ulysse, C. and Shihab, S. and Lemaître, A. and Kim, J.-V. and Jeudy, V. and Gourdon, C.}},
issn = {{2469-9950}},
journal = {{Physical Review B}},
number = {{5}},
publisher = {{American Physical Society (APS)}},
title = {{{Spin transfer and spin-orbit torques in in-plane magnetized (Ga,Mn)As tracks}}},
doi = {{10.1103/physrevb.95.054422}},
volume = {{95}},
year = {{2017}},
}
@article{59497,
abstract = {{High-quality Al/InAs and Nb/InAs superconducting hybrid structure interfaces on catalyst free InAs nanowires.
}},
author = {{Güsken, Nicholas Alexander and Rieger, Torsten and Zellekens, Patrick and Bennemann, Benjamin and Neumann, Elmar and Lepsa, Mihail I. and Schäpers, Thomas and Grützmacher, Detlev}},
issn = {{2040-3364}},
journal = {{Nanoscale}},
number = {{43}},
pages = {{16735--16741}},
publisher = {{Royal Society of Chemistry (RSC)}},
title = {{{MBE growth of Al/InAs and Nb/InAs superconducting hybrid nanowire structures}}},
doi = {{10.1039/c7nr03982d}},
volume = {{9}},
year = {{2017}},
}
@inproceedings{58786,
author = {{Wirth, Robert}},
booktitle = {{Imperial Middlebrow: Cross-colonial encounters and expressions of power in middlebrow literature and culture, 1890-1940}},
title = {{{Notions of India in A.J. Cronin’s Hatter’s Castle}}},
year = {{2017}},
}
@inproceedings{58787,
author = {{Wirth, Robert}},
booktitle = {{Britain in Europe / Europe in Britain}},
title = {{{Putting the ‘Great’ Back Into Great Britain}}},
year = {{2017}},
}
@misc{58777,
booktitle = {{Litteraria Pragensia: Studies in Literature and Culture}},
editor = {{Procházka, Martin and Poncarová, Petra Johana}},
issn = {{0862-8424}},
number = {{53}},
pages = {{101--122}},
title = {{{Cultural and Textual Appropriation in Alan Bissett's Boyracers}}},
volume = {{27}},
year = {{2017}},
}
@article{64888,
abstract = {{AbstractManche boranbasierten frustrierten Lewis‐Paare spalten Wasserstoff – wie, war bislang unklar. Um Struktur und Reaktivität in Beziehung zu setzen, werden quantenchemische Untersuchungen und NMR‐Experimente kombiniert. Sind pKa‐Werte der Lewis‐Base bekannt, lässt sich damit Reaktivität vorhersagen.}},
author = {{Paradies, Jan}},
issn = {{1439-9598}},
journal = {{Nachrichten aus der Chemie}},
number = {{2}},
pages = {{118--122}},
publisher = {{Wiley}},
title = {{{Reaktivität verstehen, ohne die Katalysatorstruktur zu kennen}}},
doi = {{10.1002/nadc.20174055283}},
volume = {{65}},
year = {{2017}},
}
@article{64899,
author = {{Straub, Bernd F. and Andexer, Jennifer and Arenz, Christoph and Beifuss, Uwe and Beuerle, Florian and Brasholz, Malte and Breinbauer, Rolf and Ditrich, Klaus and Gulder, Tobias A. M. and Hüttel, Wolfgang and Kordes, Markus and Krueger, Anke and Lehmann, Matthias and Lindel, Thomas and Luy, Burkhard and Meier, Michael A. R. and Mück-Lichtenfeld, Christian and Muhle-Goll, Claudia and Müller, Thomas J. J. and Narine, Arun and Paradies, Jan and Pfau, Roland and Pietruszka, Jörg and Schaschke, Norbert and Senge, Mathias O. and Werner, Thomas and Werz, Daniel B. and Winter, Christian A. and Worgull, Dennis}},
issn = {{1439-9598}},
journal = {{Nachrichten aus der Chemie}},
number = {{3}},
pages = {{266--304}},
publisher = {{Wiley}},
title = {{{Organische Chemie 2016}}},
doi = {{10.1002/nadc.20174059831}},
volume = {{65}},
year = {{2017}},
}
@inbook{64900,
author = {{Paradies, Jan}},
booktitle = {{Topics in Organometallic Chemistry}},
isbn = {{9783319708041}},
issn = {{1436-6002}},
publisher = {{Springer International Publishing}},
title = {{{Chiral Borane-Based Lewis Acids for Metal Free Hydrogenations}}},
doi = {{10.1007/3418_2016_173}},
year = {{2017}},
}
@misc{64964,
author = {{Mersch, Katharina Ulrike}},
booktitle = {{Historische Zeitschrift}},
number = {{2}},
pages = {{432--433}},
title = {{{Franz-Josef Arlinghaus (Ed.), Forms of Individuality and Literacy in the Medieval and Early Modern Periods, Turnhout, Brepols Publishers, 2015}}},
volume = {{304}},
year = {{2017}},
}
@inbook{65320,
author = {{Droß-Krüpe, Kerstin}},
booktitle = {{Sinews of Empire: Networks and Regional Interaction in the Roman Near East and Beyond}},
editor = {{Heldaas Seland, E. and Teigen, H.}},
pages = {{155--165}},
title = {{{Businessmen and Local Elites in the Lycos Valley}}},
year = {{2017}},
}
@inbook{65321,
author = {{Droß-Krüpe, Kerstin}},
booktitle = {{Great Women on Stage. The Reception of Women Monarchs from Antiquity in Baroque Opera}},
editor = {{Droß-Krüpe, K.}},
pages = {{9--16}},
title = {{{Great Women on Stage. The Reception of Women Monarchs from Antiquity in Baroque Opera}}},
year = {{2017}},
}
@inbook{65319,
author = {{Droß-Krüpe, Kerstin and Wild, John Peter }},
booktitle = {{Textile Terminologies from the Orient to the Mediterranean and Europe 1000 BC - AD 1000}},
editor = {{Nosch, M.-L. and Michel, C. and Gaspa, S.}},
pages = {{301--320}},
title = {{{Ars polymita, ars plumaria: the Weaving Terminology of Taqueté and Tapestry}}},
year = {{2017}},
}
@inbook{65318,
author = {{Droß-Krüpe, Kerstin}},
booktitle = {{Textile Terminologies from the Orient to the Mediterranean and Europe 1000 BC - AD 1000}},
editor = {{Nosch, M.-L. and Michel, C. and Gaspa, S.}},
pages = {{295--300}},
title = {{{χιτών - δαλματική - μαφόρτης - σύνθεσις. Common and Uncommon Garment Terms in Roman Egypt}}},
year = {{2017}},
}
@article{65317,
author = {{Droß-Krüpe, Kerstin}},
journal = {{MBAH}},
pages = {{109--122}},
title = {{{Die Pacht von gewerblichen Räumen im römischen Ägypten - Prinzipale und Agenten?}}},
volume = {{35}},
year = {{2017}},
}