---
_id: '13347'
abstract:
- lang: eng
  text: "<jats:p>&lt;div&gt;\r\n\t\t\t&lt;div&gt;\r\n\t\t\t\t&lt;div&gt;\r\n\t\t\t\t\t&lt;p&gt;Molecular
    doping in conjugated polymers is a crucial process for their application in organic\r\nphotovoltaics
    and optoelectronics. In the present work we theoretically investigate p-type molecu-\r\nlar
    doping in a series of (poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b”]dithiophene)-alt-\r\n4,7-(2,1,3-benzothiadiazole)]
    (PCPDT-BT) conjugated oligomers with different lengths and three\r\nwidely-used
    dopants with different electron affinities, namely F4TCNQ, F6TCNNQ, and CN6-CP.\r\nWe
    study in detail the molecular geometry of possible oligomer-dopant complexes and
    its influence\r\non the doping mechanisms and electronic system properties. We
    find that the mechanisms of dop-\r\ning and charge transfer observed sensitively
    depend on the specific geometry of the oligomer-dopant\r\ncomplexes. For a given
    complex different geometries may exist, some of which show transfer of\r\nan entire
    electron from the oligomer chain onto the dopant molecule resulting in an integer-charge\r\ntransfer
    complex, leaving the system in a ground state with broken spin symmetry. In other
    ge-\r\nometries merely hybridization of oligomer and dopant frontier orbitals
    occurs with partial charge\r\ntransfer but spin-symmetric ground state. Considering
    the resulting electronic density of states both\r\ncases may well contribute to
    an increased electrical conductivity of corresponding film samples while\r\nthe
    underlying physical mechanisms are entirely different.\r\n&lt;/p&gt;\r\n\t\t\t\t&lt;/div&gt;\r\n\t\t\t&lt;/div&gt;\r\n\t\t&lt;/div&gt;</jats:p>"
author:
- first_name: Chuan-Ding
  full_name: Dong, Chuan-Ding
  id: '67188'
  last_name: Dong
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
citation:
  ama: 'Dong C-D, Schumacher S. Molecular Doping of PCPDT-BT Copolymers: Comparison
    of Molecular Complexes with and Without Integer Charge Transfer. Published online
    2019.'
  apa: 'Dong, C.-D., &#38; Schumacher, S. (2019). <i>Molecular Doping of PCPDT-BT
    Copolymers: Comparison of Molecular Complexes with and Without Integer Charge
    Transfer</i>.'
  bibtex: '@article{Dong_Schumacher_2019, title={Molecular Doping of PCPDT-BT Copolymers:
    Comparison of Molecular Complexes with and Without Integer Charge Transfer}, author={Dong,
    Chuan-Ding and Schumacher, Stefan}, year={2019} }'
  chicago: 'Dong, Chuan-Ding, and Stefan Schumacher. “Molecular Doping of PCPDT-BT
    Copolymers: Comparison of Molecular Complexes with and Without Integer Charge
    Transfer,” 2019.'
  ieee: 'C.-D. Dong and S. Schumacher, “Molecular Doping of PCPDT-BT Copolymers: Comparison
    of Molecular Complexes with and Without Integer Charge Transfer.” 2019.'
  mla: 'Dong, Chuan-Ding, and Stefan Schumacher. <i>Molecular Doping of PCPDT-BT Copolymers:
    Comparison of Molecular Complexes with and Without Integer Charge Transfer</i>.
    2019.'
  short: C.-D. Dong, S. Schumacher, (2019).
date_created: 2019-09-19T13:44:34Z
date_updated: 2025-12-05T14:31:11Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '230'
- _id: '35'
- _id: '27'
language:
- iso: eng
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication_status: published
status: public
title: 'Molecular Doping of PCPDT-BT Copolymers: Comparison of Molecular Complexes
  with and Without Integer Charge Transfer'
type: preprint
user_id: '16199'
year: '2019'
...
---
_id: '13343'
author:
- first_name: Joachim
  full_name: Vollbrecht, Joachim
  last_name: Vollbrecht
- first_name: Christian
  full_name: Wiebeler, Christian
  last_name: Wiebeler
- first_name: Harald
  full_name: Bock, Harald
  last_name: Bock
- first_name: Stefan
  full_name: Schumacher, Stefan
  id: '27271'
  last_name: Schumacher
  orcid: 0000-0003-4042-4951
- first_name: Heinz-Siegfried
  full_name: Kitzerow, Heinz-Siegfried
  id: '254'
  last_name: Kitzerow
citation:
  ama: 'Vollbrecht J, Wiebeler C, Bock H, Schumacher S, Kitzerow H-S. Curved Polar
    Dibenzocoronene Esters and Imides versus Their Planar Centrosymmetric Homologs:
    Photophysical and Optoelectronic Analysis. <i>The Journal of Physical Chemistry
    C</i>. 2019;123(7):4483-4492. doi:<a href="https://doi.org/10.1021/acs.jpcc.8b10730">10.1021/acs.jpcc.8b10730</a>'
  apa: 'Vollbrecht, J., Wiebeler, C., Bock, H., Schumacher, S., &#38; Kitzerow, H.-S.
    (2019). Curved Polar Dibenzocoronene Esters and Imides versus Their Planar Centrosymmetric
    Homologs: Photophysical and Optoelectronic Analysis. <i>The Journal of Physical
    Chemistry C</i>, <i>123</i>(7), 4483–4492. <a href="https://doi.org/10.1021/acs.jpcc.8b10730">https://doi.org/10.1021/acs.jpcc.8b10730</a>'
  bibtex: '@article{Vollbrecht_Wiebeler_Bock_Schumacher_Kitzerow_2019, title={Curved
    Polar Dibenzocoronene Esters and Imides versus Their Planar Centrosymmetric Homologs:
    Photophysical and Optoelectronic Analysis}, volume={123}, DOI={<a href="https://doi.org/10.1021/acs.jpcc.8b10730">10.1021/acs.jpcc.8b10730</a>},
    number={7}, journal={The Journal of Physical Chemistry C}, author={Vollbrecht,
    Joachim and Wiebeler, Christian and Bock, Harald and Schumacher, Stefan and Kitzerow,
    Heinz-Siegfried}, year={2019}, pages={4483–4492} }'
  chicago: 'Vollbrecht, Joachim, Christian Wiebeler, Harald Bock, Stefan Schumacher,
    and Heinz-Siegfried Kitzerow. “Curved Polar Dibenzocoronene Esters and Imides
    versus Their Planar Centrosymmetric Homologs: Photophysical and Optoelectronic
    Analysis.” <i>The Journal of Physical Chemistry C</i> 123, no. 7 (2019): 4483–92.
    <a href="https://doi.org/10.1021/acs.jpcc.8b10730">https://doi.org/10.1021/acs.jpcc.8b10730</a>.'
  ieee: 'J. Vollbrecht, C. Wiebeler, H. Bock, S. Schumacher, and H.-S. Kitzerow, “Curved
    Polar Dibenzocoronene Esters and Imides versus Their Planar Centrosymmetric Homologs:
    Photophysical and Optoelectronic Analysis,” <i>The Journal of Physical Chemistry
    C</i>, vol. 123, no. 7, pp. 4483–4492, 2019, doi: <a href="https://doi.org/10.1021/acs.jpcc.8b10730">10.1021/acs.jpcc.8b10730</a>.'
  mla: 'Vollbrecht, Joachim, et al. “Curved Polar Dibenzocoronene Esters and Imides
    versus Their Planar Centrosymmetric Homologs: Photophysical and Optoelectronic
    Analysis.” <i>The Journal of Physical Chemistry C</i>, vol. 123, no. 7, 2019,
    pp. 4483–92, doi:<a href="https://doi.org/10.1021/acs.jpcc.8b10730">10.1021/acs.jpcc.8b10730</a>.'
  short: J. Vollbrecht, C. Wiebeler, H. Bock, S. Schumacher, H.-S. Kitzerow, The Journal
    of Physical Chemistry C 123 (2019) 4483–4492.
date_created: 2019-09-19T13:36:01Z
date_updated: 2025-12-05T14:29:56Z
department:
- _id: '15'
- _id: '170'
- _id: '297'
- _id: '313'
- _id: '230'
- _id: '35'
- _id: '27'
- _id: '2'
doi: 10.1021/acs.jpcc.8b10730
intvolume: '       123'
issue: '7'
language:
- iso: eng
page: 4483-4492
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: The Journal of Physical Chemistry C
publication_identifier:
  issn:
  - 1932-7447
  - 1932-7455
publication_status: published
status: public
title: 'Curved Polar Dibenzocoronene Esters and Imides versus Their Planar Centrosymmetric
  Homologs: Photophysical and Optoelectronic Analysis'
type: journal_article
user_id: '16199'
volume: 123
year: '2019'
...
---
_id: '50496'
abstract:
- lang: ger
  text: "Trotz hoher Aktualität und steigender Bedeutung liegen zum Thema Digitalisierung
    im Sportverein bisher kaum empirische Erkenntnisse vor. Der vorliegende Beitrag
    setzt sich mit folgenden Fragestellungen auseinander: (i) In welchem Umfang und
    zu welchem Zweck nutzen Sportvereine digitale Instrumente? (ii) Welche vereinsspezifischen
    Faktoren determinieren das jeweilige Nutzungsverhalten? Hierzu wurde eine Stichprobe
    von n=787 Sportvereinen aus Österreich und Deutschland generiert. Es zeigt sich,
    dass digitale Instrumente vor allem zur internen und externen Kommunikation sowie
    zur Bewältigung klassischer Verwaltungsaufgaben eingesetzt werden. Das Ausmaß
    der Nutzung hängt einerseits von vereinsexternen Bedingungen ab. So zeigt sich
    dahingehend ein Ländereffekt, dass in Deutschland digitale Instrumente stärker
    genutzt werden als in Österreich. Darüber hinaus haben Auflagen seitens der Verbände
    zur Verwendung bestimmter Software (z.B. für die Meldung von Wettkampfergebnissen)
    einen wichtigen Einfluss. Andererseits bestimmen vereinsinterne Faktoren wesentlich
    das Nutzungsverhalten. Positiv wirken vor allem die Vereinsziele ‚Engagement/Erfolg
    im Leistungssport‘ und ‚Wollen Vorreiterrolle bei der Digitalisierung einnehmen‘.
    Negativ wirken eine fehlende Strategie im Umgang mit digitalen Instrumenten sowie
    die Einschätzung, dass digitale Prozesse nicht zur eigenen Vereinskultur passen.\r\n"
author:
- first_name: Lars
  full_name: Riedl, Lars
  id: '31513'
  last_name: Riedl
- first_name: Peter
  full_name: "\tEhnold, Peter"
  last_name: "\tEhnold"
- first_name: 'Torsten '
  full_name: 'Schlesinger, Torsten '
  last_name: Schlesinger
citation:
  ama: "Riedl L, \tEhnold P, Schlesinger T. Digitalisierung im organisierten Sport.
    Eine Analyse zur Nutzung digitaler Instrumente in Sportvereinen. <i>Sciamus -
    Sport und Management</i>. 2019;(4):21-40. doi:<a href=\"https://doi.org/10.24403/jp.1016426\">10.24403/jp.1016426</a>"
  apa: "Riedl, L., \tEhnold, P., &#38; Schlesinger, T. (2019). Digitalisierung im
    organisierten Sport. Eine Analyse zur Nutzung digitaler Instrumente in Sportvereinen.
    <i>Sciamus - Sport und Management</i>, <i>4</i>, 21–40. <a href=\"https://doi.org/10.24403/jp.1016426\">https://doi.org/10.24403/jp.1016426</a>"
  bibtex: "@article{Riedl_\tEhnold_Schlesinger_2019, title={Digitalisierung im organisierten
    Sport. Eine Analyse zur Nutzung digitaler Instrumente in Sportvereinen}, DOI={<a
    href=\"https://doi.org/10.24403/jp.1016426\">10.24403/jp.1016426</a>}, number={4},
    journal={Sciamus - Sport und Management}, author={Riedl, Lars and \tEhnold, Peter
    and Schlesinger, Torsten }, year={2019}, pages={21–40} }"
  chicago: "Riedl, Lars, Peter \tEhnold, and Torsten  Schlesinger. “Digitalisierung
    im organisierten Sport. Eine Analyse zur Nutzung digitaler Instrumente in Sportvereinen.”
    <i>Sciamus - Sport und Management</i>, no. 4 (2019): 21–40. <a href=\"https://doi.org/10.24403/jp.1016426\">https://doi.org/10.24403/jp.1016426</a>."
  ieee: "L. Riedl, P. \tEhnold, and T. Schlesinger, “Digitalisierung im organisierten
    Sport. Eine Analyse zur Nutzung digitaler Instrumente in Sportvereinen,” <i>Sciamus
    - Sport und Management</i>, no. 4, pp. 21–40, 2019, doi: <a href=\"https://doi.org/10.24403/jp.1016426\">10.24403/jp.1016426</a>."
  mla: Riedl, Lars, et al. “Digitalisierung im organisierten Sport. Eine Analyse zur
    Nutzung digitaler Instrumente in Sportvereinen.” <i>Sciamus - Sport und Management</i>,
    no. 4, 2019, pp. 21–40, doi:<a href="https://doi.org/10.24403/jp.1016426">10.24403/jp.1016426</a>.
  short: "L. Riedl, P. \tEhnold, T. Schlesinger, Sciamus - Sport und Management (2019)
    21–40."
date_created: 2024-01-15T10:05:29Z
date_updated: 2025-12-10T15:58:12Z
department:
- _id: '175'
doi: 10.24403/jp.1016426
issue: '4'
language:
- iso: ger
main_file_link:
- open_access: '1'
  url: https://zs.thulb.uni-jena.de/servlets/MCRFileNodeServlet/jportal_derivate_00292234/SSuM_Ausgabe_4_2019_Sonderausgabe_Aktuell_021_040.pdf
oa: '1'
page: 21-40
publication: Sciamus - Sport und Management
publication_identifier:
  issn:
  - 1869-8247
publication_status: published
status: public
title: Digitalisierung im organisierten Sport. Eine Analyse zur Nutzung digitaler
  Instrumente in Sportvereinen
type: journal_article
user_id: '31513'
year: '2019'
...
---
_id: '23764'
author:
- first_name: Franziska
  full_name: Kehne, Franziska
  last_name: Kehne
- first_name: Sabine
  full_name: Fechner, Sabine
  id: '54823'
  last_name: Fechner
  orcid: 0000-0001-5645-5870
citation:
  ama: 'Kehne F, Fechner S. Enkodierung chemischer Konzepte aus lebenweltlichen Kontexten.
    In: Maurer C, ed. <i>Naturwissenschaftliche Bildung als Grundlage für berufliche
    und gesellschaftliche Teilhabe. Gesellschaft für Didaktik der Chemie und Physik,
    Jahrestagung in Kiel 2018</i>. Universität Regensburg; 2019:755-758.'
  apa: Kehne, F., &#38; Fechner, S. (2019). Enkodierung chemischer Konzepte aus lebenweltlichen
    Kontexten. In C. Maurer (Ed.), <i>Naturwissenschaftliche Bildung als Grundlage
    für berufliche und gesellschaftliche Teilhabe. Gesellschaft für Didaktik der Chemie
    und Physik, Jahrestagung in Kiel 2018</i> (pp. 755–758). Universität Regensburg.
  bibtex: '@inproceedings{Kehne_Fechner_2019, title={Enkodierung chemischer Konzepte
    aus lebenweltlichen Kontexten}, booktitle={Naturwissenschaftliche Bildung als
    Grundlage für berufliche und gesellschaftliche Teilhabe. Gesellschaft für Didaktik
    der Chemie und Physik, Jahrestagung in Kiel 2018}, publisher={Universität Regensburg},
    author={Kehne, Franziska and Fechner, Sabine}, editor={Maurer, Christian }, year={2019},
    pages={755–758} }'
  chicago: Kehne, Franziska, and Sabine Fechner. “Enkodierung chemischer Konzepte
    aus lebenweltlichen Kontexten.” In <i>Naturwissenschaftliche Bildung als Grundlage
    für berufliche und gesellschaftliche Teilhabe. Gesellschaft für Didaktik der Chemie
    und Physik, Jahrestagung in Kiel 2018</i>, edited by Christian  Maurer, 755–58.
    Universität Regensburg, 2019.
  ieee: F. Kehne and S. Fechner, “Enkodierung chemischer Konzepte aus lebenweltlichen
    Kontexten,” in <i>Naturwissenschaftliche Bildung als Grundlage für berufliche
    und gesellschaftliche Teilhabe. Gesellschaft für Didaktik der Chemie und Physik,
    Jahrestagung in Kiel 2018</i>, 2019, pp. 755–758.
  mla: Kehne, Franziska, and Sabine Fechner. “Enkodierung chemischer Konzepte aus
    lebenweltlichen Kontexten.” <i>Naturwissenschaftliche Bildung als Grundlage für
    berufliche und gesellschaftliche Teilhabe. Gesellschaft für Didaktik der Chemie
    und Physik, Jahrestagung in Kiel 2018</i>, edited by Christian  Maurer, Universität
    Regensburg, 2019, pp. 755–58.
  short: 'F. Kehne, S. Fechner, in: C. Maurer (Ed.), Naturwissenschaftliche Bildung
    als Grundlage für berufliche und gesellschaftliche Teilhabe. Gesellschaft für
    Didaktik der Chemie und Physik, Jahrestagung in Kiel 2018, Universität Regensburg,
    2019, pp. 755–758.'
date_created: 2021-09-03T17:43:47Z
date_updated: 2025-12-11T13:41:23Z
department:
- _id: '386'
- _id: '33'
editor:
- first_name: 'Christian '
  full_name: 'Maurer, Christian '
  last_name: Maurer
language:
- iso: ger
main_file_link:
- url: https://gdcp-ev.de/wp-content/tb2019/TB2019_755_Kehne.pdf
page: 755-758
publication: Naturwissenschaftliche Bildung als Grundlage für berufliche und gesellschaftliche
  Teilhabe. Gesellschaft für Didaktik der Chemie und Physik, Jahrestagung in Kiel
  2018
publisher: Universität Regensburg
status: public
title: Enkodierung chemischer Konzepte aus lebenweltlichen Kontexten
type: conference
user_id: '54823'
year: '2019'
...
---
_id: '62824'
author:
- first_name: Franziska
  full_name: Kehne, Franziska
  last_name: Kehne
citation:
  ama: Kehne F. <i>Analyse Des Transfers von Kontextualisiert Erworbenem Wissen Im
    Fach Chemie</i>. Logos Verlag; 2019.
  apa: Kehne, F. (2019). <i>Analyse des Transfers von kontextualisiert erworbenem
    Wissen im Fach Chemie</i>. Logos Verlag.
  bibtex: '@book{Kehne_2019, place={Berlin}, title={Analyse des Transfers von kontextualisiert
    erworbenem Wissen im Fach Chemie}, publisher={Logos Verlag}, author={Kehne, Franziska},
    year={2019} }'
  chicago: 'Kehne, Franziska. <i>Analyse Des Transfers von Kontextualisiert Erworbenem
    Wissen Im Fach Chemie</i>. Berlin: Logos Verlag, 2019.'
  ieee: 'F. Kehne, <i>Analyse des Transfers von kontextualisiert erworbenem Wissen
    im Fach Chemie</i>. Berlin: Logos Verlag, 2019.'
  mla: Kehne, Franziska. <i>Analyse Des Transfers von Kontextualisiert Erworbenem
    Wissen Im Fach Chemie</i>. Logos Verlag, 2019.
  short: F. Kehne, Analyse Des Transfers von Kontextualisiert Erworbenem Wissen Im
    Fach Chemie, Logos Verlag, Berlin, 2019.
date_created: 2025-12-03T21:32:57Z
date_updated: 2025-12-11T13:40:52Z
department:
- _id: '386'
- _id: '33'
language:
- iso: eng
main_file_link:
- url: https://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=4846&lng=deu&id=
place: Berlin
publisher: Logos Verlag
status: public
supervisor:
- first_name: Sabine
  full_name: Fechner, Sabine
  id: '54823'
  last_name: Fechner
  orcid: 0000-0001-5645-5870
title: Analyse des Transfers von kontextualisiert erworbenem Wissen im Fach Chemie
type: dissertation
user_id: '54823'
year: '2019'
...
---
_id: '59500'
article_number: '179'
author:
- first_name: Nicholas Alexander
  full_name: Güsken, Nicholas Alexander
  id: '112030'
  last_name: Güsken
  orcid: 0000-0002-4816-0666
- first_name: Torsten
  full_name: Rieger, Torsten
  last_name: Rieger
- first_name: Gregor
  full_name: Mussler, Gregor
  last_name: Mussler
- first_name: Mihail Ion
  full_name: Lepsa, Mihail Ion
  last_name: Lepsa
- first_name: Detlev
  full_name: Grützmacher, Detlev
  last_name: Grützmacher
citation:
  ama: Güsken NA, Rieger T, Mussler G, Lepsa MI, Grützmacher D. Influence of Te-Doping
    on Catalyst-Free VS InAs Nanowires. <i>Nanoscale Research Letters</i>. 2019;14(1).
    doi:<a href="https://doi.org/10.1186/s11671-019-3004-0">10.1186/s11671-019-3004-0</a>
  apa: Güsken, N. A., Rieger, T., Mussler, G., Lepsa, M. I., &#38; Grützmacher, D.
    (2019). Influence of Te-Doping on Catalyst-Free VS InAs Nanowires. <i>Nanoscale
    Research Letters</i>, <i>14</i>(1), Article 179. <a href="https://doi.org/10.1186/s11671-019-3004-0">https://doi.org/10.1186/s11671-019-3004-0</a>
  bibtex: '@article{Güsken_Rieger_Mussler_Lepsa_Grützmacher_2019, title={Influence
    of Te-Doping on Catalyst-Free VS InAs Nanowires}, volume={14}, DOI={<a href="https://doi.org/10.1186/s11671-019-3004-0">10.1186/s11671-019-3004-0</a>},
    number={1179}, journal={Nanoscale Research Letters}, publisher={Springer Science
    and Business Media LLC}, author={Güsken, Nicholas Alexander and Rieger, Torsten
    and Mussler, Gregor and Lepsa, Mihail Ion and Grützmacher, Detlev}, year={2019}
    }'
  chicago: Güsken, Nicholas Alexander, Torsten Rieger, Gregor Mussler, Mihail Ion
    Lepsa, and Detlev Grützmacher. “Influence of Te-Doping on Catalyst-Free VS InAs
    Nanowires.” <i>Nanoscale Research Letters</i> 14, no. 1 (2019). <a href="https://doi.org/10.1186/s11671-019-3004-0">https://doi.org/10.1186/s11671-019-3004-0</a>.
  ieee: 'N. A. Güsken, T. Rieger, G. Mussler, M. I. Lepsa, and D. Grützmacher, “Influence
    of Te-Doping on Catalyst-Free VS InAs Nanowires,” <i>Nanoscale Research Letters</i>,
    vol. 14, no. 1, Art. no. 179, 2019, doi: <a href="https://doi.org/10.1186/s11671-019-3004-0">10.1186/s11671-019-3004-0</a>.'
  mla: Güsken, Nicholas Alexander, et al. “Influence of Te-Doping on Catalyst-Free
    VS InAs Nanowires.” <i>Nanoscale Research Letters</i>, vol. 14, no. 1, 179, Springer
    Science and Business Media LLC, 2019, doi:<a href="https://doi.org/10.1186/s11671-019-3004-0">10.1186/s11671-019-3004-0</a>.
  short: N.A. Güsken, T. Rieger, G. Mussler, M.I. Lepsa, D. Grützmacher, Nanoscale
    Research Letters 14 (2019).
date_created: 2025-04-10T13:26:06Z
date_updated: 2025-12-15T11:22:09Z
doi: 10.1186/s11671-019-3004-0
intvolume: '        14'
issue: '1'
language:
- iso: eng
publication: Nanoscale Research Letters
publication_identifier:
  issn:
  - 1931-7573
  - 1556-276X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Influence of Te-Doping on Catalyst-Free VS InAs Nanowires
type: journal_article
user_id: '112030'
volume: 14
year: '2019'
...
---
_id: '40384'
article_number: '053829'
author:
- first_name: Alessandro
  full_name: Ferreri, Alessandro
  id: '65609'
  last_name: Ferreri
- first_name: V.
  full_name: Ansari, V.
  last_name: Ansari
- first_name: Christine
  full_name: Silberhorn, Christine
  id: '26263'
  last_name: Silberhorn
- first_name: Polina R.
  full_name: Sharapova, Polina R.
  id: '60286'
  last_name: Sharapova
citation:
  ama: Ferreri A, Ansari V, Silberhorn C, Sharapova PR. Temporally multimode four-photon
    Hong-Ou-Mandel interference. <i>Physical Review A</i>. 2019;100(5). doi:<a href="https://doi.org/10.1103/physreva.100.053829">10.1103/physreva.100.053829</a>
  apa: Ferreri, A., Ansari, V., Silberhorn, C., &#38; Sharapova, P. R. (2019). Temporally
    multimode four-photon Hong-Ou-Mandel interference. <i>Physical Review A</i>, <i>100</i>(5),
    Article 053829. <a href="https://doi.org/10.1103/physreva.100.053829">https://doi.org/10.1103/physreva.100.053829</a>
  bibtex: '@article{Ferreri_Ansari_Silberhorn_Sharapova_2019, title={Temporally multimode
    four-photon Hong-Ou-Mandel interference}, volume={100}, DOI={<a href="https://doi.org/10.1103/physreva.100.053829">10.1103/physreva.100.053829</a>},
    number={5053829}, journal={Physical Review A}, publisher={American Physical Society
    (APS)}, author={Ferreri, Alessandro and Ansari, V. and Silberhorn, Christine and
    Sharapova, Polina R.}, year={2019} }'
  chicago: Ferreri, Alessandro, V. Ansari, Christine Silberhorn, and Polina R. Sharapova.
    “Temporally Multimode Four-Photon Hong-Ou-Mandel Interference.” <i>Physical Review
    A</i> 100, no. 5 (2019). <a href="https://doi.org/10.1103/physreva.100.053829">https://doi.org/10.1103/physreva.100.053829</a>.
  ieee: 'A. Ferreri, V. Ansari, C. Silberhorn, and P. R. Sharapova, “Temporally multimode
    four-photon Hong-Ou-Mandel interference,” <i>Physical Review A</i>, vol. 100,
    no. 5, Art. no. 053829, 2019, doi: <a href="https://doi.org/10.1103/physreva.100.053829">10.1103/physreva.100.053829</a>.'
  mla: Ferreri, Alessandro, et al. “Temporally Multimode Four-Photon Hong-Ou-Mandel
    Interference.” <i>Physical Review A</i>, vol. 100, no. 5, 053829, American Physical
    Society (APS), 2019, doi:<a href="https://doi.org/10.1103/physreva.100.053829">10.1103/physreva.100.053829</a>.
  short: A. Ferreri, V. Ansari, C. Silberhorn, P.R. Sharapova, Physical Review A 100
    (2019).
date_created: 2023-01-26T14:12:28Z
date_updated: 2025-12-16T11:28:33Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '288'
- _id: '230'
- _id: '429'
- _id: '35'
doi: 10.1103/physreva.100.053829
intvolume: '       100'
issue: '5'
language:
- iso: eng
project:
- _id: '53'
  name: 'TRR 142: TRR 142'
- _id: '56'
  name: 'TRR 142 - C: TRR 142 - Project Area C'
- _id: '72'
  name: 'TRR 142 - C2: TRR 142 - Subproject C2'
publication: Physical Review A
publication_identifier:
  issn:
  - 2469-9926
  - 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Temporally multimode four-photon Hong-Ou-Mandel interference
type: journal_article
user_id: '16199'
volume: 100
year: '2019'
...
---
_id: '63177'
author:
- first_name: M
  full_name: Ludwig, M
  last_name: Ludwig
- first_name: S
  full_name: Jablonski, S
  last_name: Jablonski
citation:
  ama: Ludwig M, Jablonski S. Doing Math Modelling Outdoors-A Special Math Class Activity
    designed with MathCityMap. Published online 2019.
  apa: Ludwig, M., &#38; Jablonski, S. (2019). <i>Doing Math Modelling Outdoors-A
    Special Math Class Activity designed with MathCityMap</i>.
  bibtex: '@article{Ludwig_Jablonski_2019, title={Doing Math Modelling Outdoors-A
    Special Math Class Activity designed with MathCityMap}, author={Ludwig, M and
    Jablonski, S}, year={2019} }'
  chicago: Ludwig, M, and S Jablonski. “Doing Math Modelling Outdoors-A Special Math
    Class Activity Designed with MathCityMap,” 2019.
  ieee: M. Ludwig and S. Jablonski, “Doing Math Modelling Outdoors-A Special Math
    Class Activity designed with MathCityMap,” 2019.
  mla: Ludwig, M., and S. Jablonski. <i>Doing Math Modelling Outdoors-A Special Math
    Class Activity Designed with MathCityMap</i>. 2019.
  short: M. Ludwig, S. Jablonski, (2019).
date_created: 2025-12-17T08:53:35Z
date_updated: 2025-12-17T08:56:11Z
publication_identifier:
  issn:
  - 978-84-9048-661-0
publication_status: published
quality_controlled: '1'
status: public
title: Doing Math Modelling Outdoors-A Special Math Class Activity designed with MathCityMap
type: journal_article
user_id: '111489'
year: '2019'
...
---
_id: '63197'
author:
- first_name: Claudia
  full_name: Decker, Claudia
  id: '31046'
  last_name: Decker
- first_name: Maria
  full_name: Mochalova, Maria
  last_name: Mochalova
citation:
  ama: 'Decker C, Mochalova M. Professionalisierung im Lehramtsstudium an der Universität
    Paderborn. In: ; 2019.'
  apa: Decker, C., &#38; Mochalova, M. (2019). <i>Professionalisierung im Lehramtsstudium
    an der Universität Paderborn</i>. Lehrer*innen als Alleskönner? Querschnittsthemen
    zwischen Professionsanspruch und De-Professionalisierung. Tagung der Hochschulen
    des Niedersächsischen Verbundes zur Lehrerbildung und der HRK, Universität Osnabrück.
  bibtex: '@inproceedings{Decker_Mochalova_2019, title={Professionalisierung im Lehramtsstudium
    an der Universität Paderborn}, author={Decker, Claudia and Mochalova, Maria},
    year={2019} }'
  chicago: Decker, Claudia, and Maria Mochalova. “Professionalisierung Im Lehramtsstudium
    an Der Universität Paderborn,” 2019.
  ieee: C. Decker and M. Mochalova, “Professionalisierung im Lehramtsstudium an der
    Universität Paderborn,” presented at the Lehrer*innen als Alleskönner? Querschnittsthemen
    zwischen Professionsanspruch und De-Professionalisierung. Tagung der Hochschulen
    des Niedersächsischen Verbundes zur Lehrerbildung und der HRK, Universität Osnabrück,
    2019.
  mla: Decker, Claudia, and Maria Mochalova. <i>Professionalisierung Im Lehramtsstudium
    an Der Universität Paderborn</i>. 2019.
  short: 'C. Decker, M. Mochalova, in: 2019.'
conference:
  location: Universität Osnabrück
  name: Lehrer*innen als Alleskönner? Querschnittsthemen zwischen Professionsanspruch
    und De-Professionalisierung. Tagung der Hochschulen des Niedersächsischen Verbundes
    zur Lehrerbildung und der HRK
  start_date: 19.9.2019
date_created: 2025-12-18T10:52:09Z
date_updated: 2025-12-18T10:52:15Z
department:
- _id: '33'
language:
- iso: eng
status: public
title: Professionalisierung im Lehramtsstudium an der Universität Paderborn
type: conference
user_id: '31046'
year: '2019'
...
---
_id: '63325'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>We consider the
    spatially 2D version of the model $$\\begin{equation*} \\qquad\\quad\\left\\{
    \\begin{array}{@{}rcll} n_t + u\\cdot\\nabla n &amp;=&amp; \\Delta n - \\nabla
    \\cdot \\big(nS(x,n,c) \\cdot \\nabla c \\big), \\qquad &amp;\\qquad x\\in \\Omega,
    \\ t&amp;gt;0, \\\\ c_t + u\\cdot \\nabla c &amp;=&amp; \\Delta c - n f(c), \\qquad
    &amp;\\qquad x\\in \\Omega, \\ t&amp;gt;0, \\\\ u_t &amp;=&amp; \\Delta u + \\nabla
    P + n\\nabla\\phi, \\qquad \\nabla\\cdot u=0, \\qquad &amp;\\qquad x\\in \\Omega,
    \\ t&amp;gt;0, \\end{array} \\right. \\qquad \\qquad (\\star) \\end{equation*}$$for
    nutrient taxis processes, possibly interacting with liquid environments. Here
    the particular focus is on the situation when the chemotactic sensitivity $S$
    is not a scalar function but rather attains general values in ${\\mathbb{R}}^{2\\times
    2}$, thus accounting for rotational flux components in accordance with experimental
    findings and recent modeling approaches. Reflecting significant new challenges
    that mainly stem from apparent loss of energy-like structures, especially for
    initial data with large size, the knowledge on ($\\star$) so far seems essentially
    restricted to results on global existence of certain generalized solutions with
    possibly quite poor boundedness and regularity properties; widely unaddressed
    seem aspects related to possible effects of such non-diagonal taxis mechanisms
    on the qualitative solution behavior, especially with regard to the fundamental
    question whether spatial structures may thereby be supported. The present work
    answers the latter in the negative in the following sense: under the assumptions
    that the initial data $(n_0,c_0,u_0)$ and the parameter functions $S$, $f$, and
    $\\phi$ are sufficiently smooth, and that $S$ is bounded and $f$ is positive on
    $(0,\\infty )$ with $f(0)=0$, it is shown that any nontrivial of these solutions
    eventually becomes smooth and satisfies $$\\begin{equation*} n(\\cdot,t)\\to -
    \\int_\\Omega n_0, \\quad c(\\cdot,t)\\to 0 \\quad \\text{and} \\quad u(\\cdot,t)\\to
    0 \\qquad \\text{as} \\ t\\to\\infty, \\end{equation*}$$uniformly with respect
    to $x\\in \\Omega$. By not requiring any smallness condition on the initial data,
    the latter seems new even in the corresponding fluid-free version obtained on
    letting $u\\equiv 0$ in ($\\star$).</jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Can Rotational Fluxes Impede the Tendency Toward Spatial Homogeneity
    in Nutrient Taxis(-Stokes) Systems? <i>International Mathematics Research Notices</i>.
    2019;2021(11):8106-8152. doi:<a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>
  apa: Winkler, M. (2019). Can Rotational Fluxes Impede the Tendency Toward Spatial
    Homogeneity in Nutrient Taxis(-Stokes) Systems? <i>International Mathematics Research
    Notices</i>, <i>2021</i>(11), 8106–8152. <a href="https://doi.org/10.1093/imrn/rnz056">https://doi.org/10.1093/imrn/rnz056</a>
  bibtex: '@article{Winkler_2019, title={Can Rotational Fluxes Impede the Tendency
    Toward Spatial Homogeneity in Nutrient Taxis(-Stokes) Systems?}, volume={2021},
    DOI={<a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>}, number={11},
    journal={International Mathematics Research Notices}, publisher={Oxford University
    Press (OUP)}, author={Winkler, Michael}, year={2019}, pages={8106–8152} }'
  chicago: 'Winkler, Michael. “Can Rotational Fluxes Impede the Tendency Toward Spatial
    Homogeneity in Nutrient Taxis(-Stokes) Systems?” <i>International Mathematics
    Research Notices</i> 2021, no. 11 (2019): 8106–52. <a href="https://doi.org/10.1093/imrn/rnz056">https://doi.org/10.1093/imrn/rnz056</a>.'
  ieee: 'M. Winkler, “Can Rotational Fluxes Impede the Tendency Toward Spatial Homogeneity
    in Nutrient Taxis(-Stokes) Systems?,” <i>International Mathematics Research Notices</i>,
    vol. 2021, no. 11, pp. 8106–8152, 2019, doi: <a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>.'
  mla: Winkler, Michael. “Can Rotational Fluxes Impede the Tendency Toward Spatial
    Homogeneity in Nutrient Taxis(-Stokes) Systems?” <i>International Mathematics
    Research Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2019,
    pp. 8106–52, doi:<a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>.
  short: M. Winkler, International Mathematics Research Notices 2021 (2019) 8106–8152.
date_created: 2025-12-18T19:35:55Z
date_updated: 2025-12-18T19:59:29Z
doi: 10.1093/imrn/rnz056
intvolume: '      2021'
issue: '11'
language:
- iso: eng
page: 8106-8152
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Can Rotational Fluxes Impede the Tendency Toward Spatial Homogeneity in Nutrient
  Taxis(-Stokes) Systems?
type: journal_article
user_id: '31496'
volume: 2021
year: '2019'
...
---
_id: '63337'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>In bounded<jats:italic>n</jats:italic>-dimensional
    domains<jats:italic>Ω</jats:italic>, the Neumann problem for the parabolic equation</jats:p><jats:p><jats:disp-formula
    id="j_anona-2020-0013_eq_001"><jats:alternatives><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink"
    xlink:href="graphic/j_anona-2020-0013_eq_001.png" position="float" orientation="portrait"
    /><jats:tex-math>$$\begin{array}{} \displaystyle u_t = \nabla \cdot \Big( A(x,t)\cdot\nabla
    u\Big) + \nabla \cdot \Big(b(x,t)u\Big) - f(x,t,u)+g(x,t) \end{array}$$</jats:tex-math></jats:alternatives><jats:label>(*)</jats:label></jats:disp-formula></jats:p><jats:p>is
    considered for sufficiently regular matrix-valued<jats:italic>A</jats:italic>,
    vector-valued<jats:italic>b</jats:italic>and real valued<jats:italic>g</jats:italic>,
    and with<jats:italic>f</jats:italic>representing superlinear absorption in generalizing
    the prototypical choice given by<jats:italic>f</jats:italic>(⋅, ⋅,<jats:italic>s</jats:italic>)
    =<jats:italic>s<jats:sup>α</jats:sup></jats:italic>with<jats:italic>α</jats:italic>&gt;
    1. Problems of this form arise in a natural manner as sub-problems in several
    applications such as cross-diffusion systems either of Keller-Segel or of Shigesada-Kawasaki-Teramoto
    type in mathematical biology, and accordingly a natural space for initial data
    appears to be<jats:italic>L</jats:italic><jats:sup>1</jats:sup>(<jats:italic>Ω</jats:italic>).</jats:p><jats:p>The
    main objective thus consists in examining how far solutions can be constructed
    for initial data merely assumed to be integrable, with major challenges potentially
    resulting from the interplay between nonlinear degradation on the one hand, and
    the possibly destabilizing drift-type action on the other in such contexts. Especially,
    the applicability of well-established methods such as techniques relying on entropy-like
    structures available in some particular cases, for instance, seems quite limited
    in the present setting, as these typically rely on higher initial regularity properties.</jats:p><jats:p>The
    first of the main results shows that in the general framework of (*), nevertheless
    certain global very weak solutions can be constructed through a limit process
    involving smooth solutions to approximate variants thereof, provided that the
    ingredients of the latter satisfy appropriate assumptions with regard to their
    stabilization behavior.</jats:p><jats:p>The second and seemingly most substantial
    part of the paper develops a method by which it can be shown, under suitably stregthened
    hypotheses on the integrability of<jats:italic>b</jats:italic>and the degradation
    parameter<jats:italic>α</jats:italic>, that the solutions obtained above in fact
    form genuine weak solutions in a naturally defined sense. This is achieved by
    properly exploiting a weak integral inequality, as satisfied by the very weak
    solution at hand, through a testing procedure that appears to be novel and of
    potentially independent interest.</jats:p><jats:p>To underline the strength of
    this approach, both these general results are thereafter applied to two specific
    cross-diffusion systems. Inter alia, this leads to a statement on global solvability
    in a logistic Keller-Segel system under the assumption<jats:italic>α</jats:italic>&gt;<jats:inline-formula><jats:alternatives><jats:inline-graphic
    xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_anona-2020-0013_eq_002.png"
    /><jats:tex-math>$\begin{array}{} \frac{2n+4}{n+4} \end{array}$</jats:tex-math></jats:alternatives></jats:inline-formula>on
    the respective degradation rate which seems substantially milder than any previously
    found condition in the literature. Apart from that, for a Shigesada-Kawasaki-Teramoto
    system some apparently first results on global solvability for<jats:italic>L</jats:italic><jats:sup>1</jats:sup>initial
    data are derived.</jats:p>
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. The role of superlinear damping in the construction of solutions
    to drift-diffusion problems with initial data in L1. <i>Advances in Nonlinear
    Analysis</i>. 2019;9(1):526-566. doi:<a href="https://doi.org/10.1515/anona-2020-0013">10.1515/anona-2020-0013</a>
  apa: Winkler, M. (2019). The role of superlinear damping in the construction of
    solutions to drift-diffusion problems with initial data in L1. <i>Advances in
    Nonlinear Analysis</i>, <i>9</i>(1), 526–566. <a href="https://doi.org/10.1515/anona-2020-0013">https://doi.org/10.1515/anona-2020-0013</a>
  bibtex: '@article{Winkler_2019, title={The role of superlinear damping in the construction
    of solutions to drift-diffusion problems with initial data in L1}, volume={9},
    DOI={<a href="https://doi.org/10.1515/anona-2020-0013">10.1515/anona-2020-0013</a>},
    number={1}, journal={Advances in Nonlinear Analysis}, publisher={Walter de Gruyter
    GmbH}, author={Winkler, Michael}, year={2019}, pages={526–566} }'
  chicago: 'Winkler, Michael. “The Role of Superlinear Damping in the Construction
    of Solutions to Drift-Diffusion Problems with Initial Data in L1.” <i>Advances
    in Nonlinear Analysis</i> 9, no. 1 (2019): 526–66. <a href="https://doi.org/10.1515/anona-2020-0013">https://doi.org/10.1515/anona-2020-0013</a>.'
  ieee: 'M. Winkler, “The role of superlinear damping in the construction of solutions
    to drift-diffusion problems with initial data in L1,” <i>Advances in Nonlinear
    Analysis</i>, vol. 9, no. 1, pp. 526–566, 2019, doi: <a href="https://doi.org/10.1515/anona-2020-0013">10.1515/anona-2020-0013</a>.'
  mla: Winkler, Michael. “The Role of Superlinear Damping in the Construction of Solutions
    to Drift-Diffusion Problems with Initial Data in L1.” <i>Advances in Nonlinear
    Analysis</i>, vol. 9, no. 1, Walter de Gruyter GmbH, 2019, pp. 526–66, doi:<a
    href="https://doi.org/10.1515/anona-2020-0013">10.1515/anona-2020-0013</a>.
  short: M. Winkler, Advances in Nonlinear Analysis 9 (2019) 526–566.
date_created: 2025-12-18T19:45:09Z
date_updated: 2025-12-18T20:01:54Z
doi: 10.1515/anona-2020-0013
intvolume: '         9'
issue: '1'
language:
- iso: eng
page: 526-566
publication: Advances in Nonlinear Analysis
publication_identifier:
  issn:
  - 2191-950X
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: The role of superlinear damping in the construction of solutions to drift-diffusion
  problems with initial data in L1
type: journal_article
user_id: '31496'
volume: 9
year: '2019'
...
---
_id: '63334'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global classical solutions to a doubly haptotactic cross-diffusion
    system modeling oncolytic virotherapy. <i>Journal of Differential Equations</i>.
    2019;268(9):4973-4997. doi:<a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>
  apa: Tao, Y., &#38; Winkler, M. (2019). Global classical solutions to a doubly haptotactic
    cross-diffusion system modeling oncolytic virotherapy. <i>Journal of Differential
    Equations</i>, <i>268</i>(9), 4973–4997. <a href="https://doi.org/10.1016/j.jde.2019.10.046">https://doi.org/10.1016/j.jde.2019.10.046</a>
  bibtex: '@article{Tao_Winkler_2019, title={Global classical solutions to a doubly
    haptotactic cross-diffusion system modeling oncolytic virotherapy}, volume={268},
    DOI={<a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>},
    number={9}, journal={Journal of Differential Equations}, publisher={Elsevier BV},
    author={Tao, Youshan and Winkler, Michael}, year={2019}, pages={4973–4997} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Classical Solutions to a Doubly
    Haptotactic Cross-Diffusion System Modeling Oncolytic Virotherapy.” <i>Journal
    of Differential Equations</i> 268, no. 9 (2019): 4973–97. <a href="https://doi.org/10.1016/j.jde.2019.10.046">https://doi.org/10.1016/j.jde.2019.10.046</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global classical solutions to a doubly haptotactic
    cross-diffusion system modeling oncolytic virotherapy,” <i>Journal of Differential
    Equations</i>, vol. 268, no. 9, pp. 4973–4997, 2019, doi: <a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Classical Solutions to a Doubly
    Haptotactic Cross-Diffusion System Modeling Oncolytic Virotherapy.” <i>Journal
    of Differential Equations</i>, vol. 268, no. 9, Elsevier BV, 2019, pp. 4973–97,
    doi:<a href="https://doi.org/10.1016/j.jde.2019.10.046">10.1016/j.jde.2019.10.046</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 268 (2019) 4973–4997.
date_created: 2025-12-18T19:40:07Z
date_updated: 2025-12-18T20:01:29Z
doi: 10.1016/j.jde.2019.10.046
intvolume: '       268'
issue: '9'
language:
- iso: eng
page: 4973-4997
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global classical solutions to a doubly haptotactic cross-diffusion system modeling
  oncolytic virotherapy
type: journal_article
user_id: '31496'
volume: 268
year: '2019'
...
---
_id: '63349'
author:
- first_name: Nicola
  full_name: Bellomo, Nicola
  last_name: Bellomo
- first_name: Kevin J.
  full_name: Painter, Kevin J.
  last_name: Painter
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Bellomo N, Painter KJ, Tao Y, Winkler M. Occurrence vs. Absence of Taxis-Driven
    Instabilities in a May--Nowak Model for Virus Infection. <i>SIAM Journal on Applied
    Mathematics</i>. 2019;79(5):1990-2010. doi:<a href="https://doi.org/10.1137/19m1250261">10.1137/19m1250261</a>
  apa: Bellomo, N., Painter, K. J., Tao, Y., &#38; Winkler, M. (2019). Occurrence
    vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection.
    <i>SIAM Journal on Applied Mathematics</i>, <i>79</i>(5), 1990–2010. <a href="https://doi.org/10.1137/19m1250261">https://doi.org/10.1137/19m1250261</a>
  bibtex: '@article{Bellomo_Painter_Tao_Winkler_2019, title={Occurrence vs. Absence
    of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection}, volume={79},
    DOI={<a href="https://doi.org/10.1137/19m1250261">10.1137/19m1250261</a>}, number={5},
    journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial
    &#38; Applied Mathematics (SIAM)}, author={Bellomo, Nicola and Painter, Kevin
    J. and Tao, Youshan and Winkler, Michael}, year={2019}, pages={1990–2010} }'
  chicago: 'Bellomo, Nicola, Kevin J. Painter, Youshan Tao, and Michael Winkler. “Occurrence
    vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection.”
    <i>SIAM Journal on Applied Mathematics</i> 79, no. 5 (2019): 1990–2010. <a href="https://doi.org/10.1137/19m1250261">https://doi.org/10.1137/19m1250261</a>.'
  ieee: 'N. Bellomo, K. J. Painter, Y. Tao, and M. Winkler, “Occurrence vs. Absence
    of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection,” <i>SIAM
    Journal on Applied Mathematics</i>, vol. 79, no. 5, pp. 1990–2010, 2019, doi:
    <a href="https://doi.org/10.1137/19m1250261">10.1137/19m1250261</a>.'
  mla: Bellomo, Nicola, et al. “Occurrence vs. Absence of Taxis-Driven Instabilities
    in a May--Nowak Model for Virus Infection.” <i>SIAM Journal on Applied Mathematics</i>,
    vol. 79, no. 5, Society for Industrial &#38; Applied Mathematics (SIAM), 2019,
    pp. 1990–2010, doi:<a href="https://doi.org/10.1137/19m1250261">10.1137/19m1250261</a>.
  short: N. Bellomo, K.J. Painter, Y. Tao, M. Winkler, SIAM Journal on Applied Mathematics
    79 (2019) 1990–2010.
date_created: 2025-12-19T10:47:32Z
date_updated: 2025-12-19T10:47:44Z
doi: 10.1137/19m1250261
intvolume: '        79'
issue: '5'
language:
- iso: eng
page: 1990-2010
publication: SIAM Journal on Applied Mathematics
publication_identifier:
  issn:
  - 0036-1399
  - 1095-712X
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model
  for Virus Infection
type: journal_article
user_id: '31496'
volume: 79
year: '2019'
...
---
_id: '63350'
article_number: '106823'
author:
- first_name: Marek
  full_name: Fila, Marek
  last_name: Fila
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Fila M, Winkler M. A Gagliardo-Nirenberg-type inequality and its applications
    to decay estimates for solutions of a degenerate parabolic equation. <i>Advances
    in Mathematics</i>. 2019;357. doi:<a href="https://doi.org/10.1016/j.aim.2019.106823">10.1016/j.aim.2019.106823</a>
  apa: Fila, M., &#38; Winkler, M. (2019). A Gagliardo-Nirenberg-type inequality and
    its applications to decay estimates for solutions of a degenerate parabolic equation.
    <i>Advances in Mathematics</i>, <i>357</i>, Article 106823. <a href="https://doi.org/10.1016/j.aim.2019.106823">https://doi.org/10.1016/j.aim.2019.106823</a>
  bibtex: '@article{Fila_Winkler_2019, title={A Gagliardo-Nirenberg-type inequality
    and its applications to decay estimates for solutions of a degenerate parabolic
    equation}, volume={357}, DOI={<a href="https://doi.org/10.1016/j.aim.2019.106823">10.1016/j.aim.2019.106823</a>},
    number={106823}, journal={Advances in Mathematics}, publisher={Elsevier BV}, author={Fila,
    Marek and Winkler, Michael}, year={2019} }'
  chicago: Fila, Marek, and Michael Winkler. “A Gagliardo-Nirenberg-Type Inequality
    and Its Applications to Decay Estimates for Solutions of a Degenerate Parabolic
    Equation.” <i>Advances in Mathematics</i> 357 (2019). <a href="https://doi.org/10.1016/j.aim.2019.106823">https://doi.org/10.1016/j.aim.2019.106823</a>.
  ieee: 'M. Fila and M. Winkler, “A Gagliardo-Nirenberg-type inequality and its applications
    to decay estimates for solutions of a degenerate parabolic equation,” <i>Advances
    in Mathematics</i>, vol. 357, Art. no. 106823, 2019, doi: <a href="https://doi.org/10.1016/j.aim.2019.106823">10.1016/j.aim.2019.106823</a>.'
  mla: Fila, Marek, and Michael Winkler. “A Gagliardo-Nirenberg-Type Inequality and
    Its Applications to Decay Estimates for Solutions of a Degenerate Parabolic Equation.”
    <i>Advances in Mathematics</i>, vol. 357, 106823, Elsevier BV, 2019, doi:<a href="https://doi.org/10.1016/j.aim.2019.106823">10.1016/j.aim.2019.106823</a>.
  short: M. Fila, M. Winkler, Advances in Mathematics 357 (2019).
date_created: 2025-12-19T10:49:35Z
date_updated: 2025-12-19T10:49:47Z
doi: 10.1016/j.aim.2019.106823
intvolume: '       357'
language:
- iso: eng
publication: Advances in Mathematics
publication_identifier:
  issn:
  - 0001-8708
publication_status: published
publisher: Elsevier BV
status: public
title: A Gagliardo-Nirenberg-type inequality and its applications to decay estimates
  for solutions of a degenerate parabolic equation
type: journal_article
user_id: '31496'
volume: 357
year: '2019'
...
---
_id: '63355'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>This work studies the two‐species
    Shigesada–Kawasaki–Teramoto model with cross‐diffusion for one species, as given by\r\n<jats:disp-formula>\r\n</jats:disp-formula>with
    positive parameters  and , and nonnegative constants  and . Beyond some statements
    on global existence, the literature apparently provides only few results on qualitative
    behavior of solutions; in particular, questions related to boundedness as well
    as to large time asymptotics in <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    xlink:href=\"#plms12276-disp-0001\" /> seem unsolved so far.</jats:p><jats:p>In
    the present paper it is <jats:italic>inter alia</jats:italic> shown that if  and
    \ is a bounded convex domain with smooth boundary, then whenever  and  are nonnegative,
    the associated Neumann initial‐boundary value problem for <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    xlink:href=\"#plms12276-disp-0001\" /> possesses a global classical solution which
    in fact is bounded in the sense that\r\n<jats:disp-formula>\r\n</jats:disp-formula>Moreover,
    the asymptotic behavior of arbitrary nonnegative solutions enjoying the boundedness
    property is studied in the general situation when  is arbitrary and  no longer
    necessarily convex. If , then in both cases  and , an explicit smallness condition
    on  is identified as sufficient for stabilization of any nontrivial solutions
    toward a corresponding unique nontrivial spatially homogeneous steady state. If
    \ and , then without any further assumption all nonzero solutions are seen to
    approach the equilibrium (0,1). As a by‐product, this particularly improves previous
    knowledge on nonexistence of nonconstant equilibria of <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    xlink:href=\"#plms12276-disp-0001\" />.</jats:p>"
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Boundedness and stabilization in a population model with
    cross‐diffusion for one species. <i>Proceedings of the London Mathematical Society</i>.
    2019;119(6):1598-1632. doi:<a href="https://doi.org/10.1112/plms.12276">10.1112/plms.12276</a>
  apa: Tao, Y., &#38; Winkler, M. (2019). Boundedness and stabilization in a population
    model with cross‐diffusion for one species. <i>Proceedings of the London Mathematical
    Society</i>, <i>119</i>(6), 1598–1632. <a href="https://doi.org/10.1112/plms.12276">https://doi.org/10.1112/plms.12276</a>
  bibtex: '@article{Tao_Winkler_2019, title={Boundedness and stabilization in a population
    model with cross‐diffusion for one species}, volume={119}, DOI={<a href="https://doi.org/10.1112/plms.12276">10.1112/plms.12276</a>},
    number={6}, journal={Proceedings of the London Mathematical Society}, publisher={Wiley},
    author={Tao, Youshan and Winkler, Michael}, year={2019}, pages={1598–1632} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Boundedness and Stabilization in a
    Population Model with Cross‐diffusion for One Species.” <i>Proceedings of the
    London Mathematical Society</i> 119, no. 6 (2019): 1598–1632. <a href="https://doi.org/10.1112/plms.12276">https://doi.org/10.1112/plms.12276</a>.'
  ieee: 'Y. Tao and M. Winkler, “Boundedness and stabilization in a population model
    with cross‐diffusion for one species,” <i>Proceedings of the London Mathematical
    Society</i>, vol. 119, no. 6, pp. 1598–1632, 2019, doi: <a href="https://doi.org/10.1112/plms.12276">10.1112/plms.12276</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Boundedness and Stabilization in a Population
    Model with Cross‐diffusion for One Species.” <i>Proceedings of the London Mathematical
    Society</i>, vol. 119, no. 6, Wiley, 2019, pp. 1598–632, doi:<a href="https://doi.org/10.1112/plms.12276">10.1112/plms.12276</a>.
  short: Y. Tao, M. Winkler, Proceedings of the London Mathematical Society 119 (2019)
    1598–1632.
date_created: 2025-12-19T10:54:01Z
date_updated: 2025-12-19T10:54:09Z
doi: 10.1112/plms.12276
intvolume: '       119'
issue: '6'
language:
- iso: eng
page: 1598-1632
publication: Proceedings of the London Mathematical Society
publication_identifier:
  issn:
  - 0024-6115
  - 1460-244X
publication_status: published
publisher: Wiley
status: public
title: Boundedness and stabilization in a population model with cross‐diffusion for
  one species
type: journal_article
user_id: '31496'
volume: 119
year: '2019'
...
---
_id: '63356'
abstract:
- lang: eng
  text: <jats:p> This work deals with a taxis cascade model for food consumption in
    two populations, namely foragers directly orienting their movement upward the
    gradients of food concentration and exploiters taking a parasitic strategy in
    search of food via tracking higher forager densities. As a consequence, the dynamics
    of both populations are adapted to the space distribution of food which is dynamically
    modified in time and space by the two populations. This model extends the classical
    one-species chemotaxis-consumption systems by additionally accounting for a second
    taxis mechanism coupled to the first in a consecutive manner. It is rigorously
    proved that for all suitably regular initial data, an associated Neumann-type
    initial-boundary value problem for the spatially one-dimensional version of this
    model possesses a globally defined bounded classical solution. Moreover, it is
    asserted that the considered two populations will approach spatially homogeneous
    distributions in the large time limit, provided that either the total population
    number of foragers or that of exploiters is appropriately small. </jats:p>
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Large time behavior in a forager–exploiter model with different
    taxis strategies for two groups in search of food. <i>Mathematical Models and
    Methods in Applied Sciences</i>. 2019;29(11):2151-2182. doi:<a href="https://doi.org/10.1142/s021820251950043x">10.1142/s021820251950043x</a>
  apa: Tao, Y., &#38; Winkler, M. (2019). Large time behavior in a forager–exploiter
    model with different taxis strategies for two groups in search of food. <i>Mathematical
    Models and Methods in Applied Sciences</i>, <i>29</i>(11), 2151–2182. <a href="https://doi.org/10.1142/s021820251950043x">https://doi.org/10.1142/s021820251950043x</a>
  bibtex: '@article{Tao_Winkler_2019, title={Large time behavior in a forager–exploiter
    model with different taxis strategies for two groups in search of food}, volume={29},
    DOI={<a href="https://doi.org/10.1142/s021820251950043x">10.1142/s021820251950043x</a>},
    number={11}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
    Scientific Pub Co Pte Ltd}, author={Tao, Youshan and Winkler, Michael}, year={2019},
    pages={2151–2182} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Large Time Behavior in a Forager–Exploiter
    Model with Different Taxis Strategies for Two Groups in Search of Food.” <i>Mathematical
    Models and Methods in Applied Sciences</i> 29, no. 11 (2019): 2151–82. <a href="https://doi.org/10.1142/s021820251950043x">https://doi.org/10.1142/s021820251950043x</a>.'
  ieee: 'Y. Tao and M. Winkler, “Large time behavior in a forager–exploiter model
    with different taxis strategies for two groups in search of food,” <i>Mathematical
    Models and Methods in Applied Sciences</i>, vol. 29, no. 11, pp. 2151–2182, 2019,
    doi: <a href="https://doi.org/10.1142/s021820251950043x">10.1142/s021820251950043x</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Large Time Behavior in a Forager–Exploiter
    Model with Different Taxis Strategies for Two Groups in Search of Food.” <i>Mathematical
    Models and Methods in Applied Sciences</i>, vol. 29, no. 11, World Scientific
    Pub Co Pte Ltd, 2019, pp. 2151–82, doi:<a href="https://doi.org/10.1142/s021820251950043x">10.1142/s021820251950043x</a>.
  short: Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 29
    (2019) 2151–2182.
date_created: 2025-12-19T10:54:36Z
date_updated: 2025-12-19T10:54:44Z
doi: 10.1142/s021820251950043x
intvolume: '        29'
issue: '11'
language:
- iso: eng
page: 2151-2182
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
  issn:
  - 0218-2025
  - 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Large time behavior in a forager–exploiter model with different taxis strategies
  for two groups in search of food
type: journal_article
user_id: '31496'
volume: 29
year: '2019'
...
---
_id: '63352'
author:
- first_name: Johannes
  full_name: Lankeit, Johannes
  last_name: Lankeit
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Lankeit J, Winkler M. Counterintuitive dependence of temporal asymptotics on
    initial decay in a nonlocal degenerate parabolic equation arising in game theory.
    <i>Israel Journal of Mathematics</i>. 2019;233(1):249-296. doi:<a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>
  apa: Lankeit, J., &#38; Winkler, M. (2019). Counterintuitive dependence of temporal
    asymptotics on initial decay in a nonlocal degenerate parabolic equation arising
    in game theory. <i>Israel Journal of Mathematics</i>, <i>233</i>(1), 249–296.
    <a href="https://doi.org/10.1007/s11856-019-1900-8">https://doi.org/10.1007/s11856-019-1900-8</a>
  bibtex: '@article{Lankeit_Winkler_2019, title={Counterintuitive dependence of temporal
    asymptotics on initial decay in a nonlocal degenerate parabolic equation arising
    in game theory}, volume={233}, DOI={<a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>},
    number={1}, journal={Israel Journal of Mathematics}, publisher={Springer Science
    and Business Media LLC}, author={Lankeit, Johannes and Winkler, Michael}, year={2019},
    pages={249–296} }'
  chicago: 'Lankeit, Johannes, and Michael Winkler. “Counterintuitive Dependence of
    Temporal Asymptotics on Initial Decay in a Nonlocal Degenerate Parabolic Equation
    Arising in Game Theory.” <i>Israel Journal of Mathematics</i> 233, no. 1 (2019):
    249–96. <a href="https://doi.org/10.1007/s11856-019-1900-8">https://doi.org/10.1007/s11856-019-1900-8</a>.'
  ieee: 'J. Lankeit and M. Winkler, “Counterintuitive dependence of temporal asymptotics
    on initial decay in a nonlocal degenerate parabolic equation arising in game theory,”
    <i>Israel Journal of Mathematics</i>, vol. 233, no. 1, pp. 249–296, 2019, doi:
    <a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>.'
  mla: Lankeit, Johannes, and Michael Winkler. “Counterintuitive Dependence of Temporal
    Asymptotics on Initial Decay in a Nonlocal Degenerate Parabolic Equation Arising
    in Game Theory.” <i>Israel Journal of Mathematics</i>, vol. 233, no. 1, Springer
    Science and Business Media LLC, 2019, pp. 249–96, doi:<a href="https://doi.org/10.1007/s11856-019-1900-8">10.1007/s11856-019-1900-8</a>.
  short: J. Lankeit, M. Winkler, Israel Journal of Mathematics 233 (2019) 249–296.
date_created: 2025-12-19T10:51:24Z
date_updated: 2025-12-19T10:51:33Z
doi: 10.1007/s11856-019-1900-8
intvolume: '       233'
issue: '1'
language:
- iso: eng
page: 249-296
publication: Israel Journal of Mathematics
publication_identifier:
  issn:
  - 0021-2172
  - 1565-8511
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal
  degenerate parabolic equation arising in game theory
type: journal_article
user_id: '31496'
volume: 233
year: '2019'
...
---
_id: '63358'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: 'Tao Y, Winkler M. A chemotaxis-haptotaxis system with haptoattractant remodeling:
    Boundedness enforced by mild saturation of signal production. <i>Communications
    on Pure &#38;amp; Applied Analysis</i>. 2019;18(4):2047-2067. doi:<a href="https://doi.org/10.3934/cpaa.2019092">10.3934/cpaa.2019092</a>'
  apa: 'Tao, Y., &#38; Winkler, M. (2019). A chemotaxis-haptotaxis system with haptoattractant
    remodeling: Boundedness enforced by mild saturation of signal production. <i>Communications
    on Pure &#38;amp; Applied Analysis</i>, <i>18</i>(4), 2047–2067. <a href="https://doi.org/10.3934/cpaa.2019092">https://doi.org/10.3934/cpaa.2019092</a>'
  bibtex: '@article{Tao_Winkler_2019, title={A chemotaxis-haptotaxis system with haptoattractant
    remodeling: Boundedness enforced by mild saturation of signal production}, volume={18},
    DOI={<a href="https://doi.org/10.3934/cpaa.2019092">10.3934/cpaa.2019092</a>},
    number={4}, journal={Communications on Pure &#38;amp; Applied Analysis}, publisher={American
    Institute of Mathematical Sciences (AIMS)}, author={Tao, Youshan and Winkler,
    Michael}, year={2019}, pages={2047–2067} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “A Chemotaxis-Haptotaxis System with
    Haptoattractant Remodeling: Boundedness Enforced by Mild Saturation of Signal
    Production.” <i>Communications on Pure &#38;amp; Applied Analysis</i> 18, no.
    4 (2019): 2047–67. <a href="https://doi.org/10.3934/cpaa.2019092">https://doi.org/10.3934/cpaa.2019092</a>.'
  ieee: 'Y. Tao and M. Winkler, “A chemotaxis-haptotaxis system with haptoattractant
    remodeling: Boundedness enforced by mild saturation of signal production,” <i>Communications
    on Pure &#38;amp; Applied Analysis</i>, vol. 18, no. 4, pp. 2047–2067, 2019, doi:
    <a href="https://doi.org/10.3934/cpaa.2019092">10.3934/cpaa.2019092</a>.'
  mla: 'Tao, Youshan, and Michael Winkler. “A Chemotaxis-Haptotaxis System with Haptoattractant
    Remodeling: Boundedness Enforced by Mild Saturation of Signal Production.” <i>Communications
    on Pure &#38;amp; Applied Analysis</i>, vol. 18, no. 4, American Institute of
    Mathematical Sciences (AIMS), 2019, pp. 2047–67, doi:<a href="https://doi.org/10.3934/cpaa.2019092">10.3934/cpaa.2019092</a>.'
  short: Y. Tao, M. Winkler, Communications on Pure &#38;amp; Applied Analysis 18
    (2019) 2047–2067.
date_created: 2025-12-19T10:56:26Z
date_updated: 2025-12-19T10:56:33Z
doi: 10.3934/cpaa.2019092
intvolume: '        18'
issue: '4'
language:
- iso: eng
page: 2047-2067
publication: Communications on Pure &amp; Applied Analysis
publication_identifier:
  issn:
  - 1553-5258
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: 'A chemotaxis-haptotaxis system with haptoattractant remodeling: Boundedness
  enforced by mild saturation of signal production'
type: journal_article
user_id: '31496'
volume: 18
year: '2019'
...
---
_id: '63357'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global smooth solvability of a parabolic–elliptic nutrient
    taxis system in domains of arbitrary dimension. <i>Journal of Differential Equations</i>.
    2019;267(1):388-406. doi:<a href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>
  apa: Tao, Y., &#38; Winkler, M. (2019). Global smooth solvability of a parabolic–elliptic
    nutrient taxis system in domains of arbitrary dimension. <i>Journal of Differential
    Equations</i>, <i>267</i>(1), 388–406. <a href="https://doi.org/10.1016/j.jde.2019.01.014">https://doi.org/10.1016/j.jde.2019.01.014</a>
  bibtex: '@article{Tao_Winkler_2019, title={Global smooth solvability of a parabolic–elliptic
    nutrient taxis system in domains of arbitrary dimension}, volume={267}, DOI={<a
    href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>},
    number={1}, journal={Journal of Differential Equations}, publisher={Elsevier BV},
    author={Tao, Youshan and Winkler, Michael}, year={2019}, pages={388–406} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Smooth Solvability of a Parabolic–Elliptic
    Nutrient Taxis System in Domains of Arbitrary Dimension.” <i>Journal of Differential
    Equations</i> 267, no. 1 (2019): 388–406. <a href="https://doi.org/10.1016/j.jde.2019.01.014">https://doi.org/10.1016/j.jde.2019.01.014</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global smooth solvability of a parabolic–elliptic
    nutrient taxis system in domains of arbitrary dimension,” <i>Journal of Differential
    Equations</i>, vol. 267, no. 1, pp. 388–406, 2019, doi: <a href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Smooth Solvability of a Parabolic–Elliptic
    Nutrient Taxis System in Domains of Arbitrary Dimension.” <i>Journal of Differential
    Equations</i>, vol. 267, no. 1, Elsevier BV, 2019, pp. 388–406, doi:<a href="https://doi.org/10.1016/j.jde.2019.01.014">10.1016/j.jde.2019.01.014</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 267 (2019) 388–406.
date_created: 2025-12-19T10:55:53Z
date_updated: 2025-12-19T10:56:01Z
doi: 10.1016/j.jde.2019.01.014
intvolume: '       267'
issue: '1'
language:
- iso: eng
page: 388-406
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global smooth solvability of a parabolic–elliptic nutrient taxis system in
  domains of arbitrary dimension
type: journal_article
user_id: '31496'
volume: 267
year: '2019'
...
---
_id: '63353'
author:
- first_name: Johannes
  full_name: Lankeit, Johannes
  last_name: Lankeit
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Lankeit J, Winkler M. Facing Low Regularity in Chemotaxis Systems. <i>Jahresbericht
    der Deutschen Mathematiker-Vereinigung</i>. 2019;122(1):35-64. doi:<a href="https://doi.org/10.1365/s13291-019-00210-z">10.1365/s13291-019-00210-z</a>
  apa: Lankeit, J., &#38; Winkler, M. (2019). Facing Low Regularity in Chemotaxis
    Systems. <i>Jahresbericht Der Deutschen Mathematiker-Vereinigung</i>, <i>122</i>(1),
    35–64. <a href="https://doi.org/10.1365/s13291-019-00210-z">https://doi.org/10.1365/s13291-019-00210-z</a>
  bibtex: '@article{Lankeit_Winkler_2019, title={Facing Low Regularity in Chemotaxis
    Systems}, volume={122}, DOI={<a href="https://doi.org/10.1365/s13291-019-00210-z">10.1365/s13291-019-00210-z</a>},
    number={1}, journal={Jahresbericht der Deutschen Mathematiker-Vereinigung}, publisher={Springer
    Fachmedien Wiesbaden GmbH}, author={Lankeit, Johannes and Winkler, Michael}, year={2019},
    pages={35–64} }'
  chicago: 'Lankeit, Johannes, and Michael Winkler. “Facing Low Regularity in Chemotaxis
    Systems.” <i>Jahresbericht Der Deutschen Mathematiker-Vereinigung</i> 122, no.
    1 (2019): 35–64. <a href="https://doi.org/10.1365/s13291-019-00210-z">https://doi.org/10.1365/s13291-019-00210-z</a>.'
  ieee: 'J. Lankeit and M. Winkler, “Facing Low Regularity in Chemotaxis Systems,”
    <i>Jahresbericht der Deutschen Mathematiker-Vereinigung</i>, vol. 122, no. 1,
    pp. 35–64, 2019, doi: <a href="https://doi.org/10.1365/s13291-019-00210-z">10.1365/s13291-019-00210-z</a>.'
  mla: Lankeit, Johannes, and Michael Winkler. “Facing Low Regularity in Chemotaxis
    Systems.” <i>Jahresbericht Der Deutschen Mathematiker-Vereinigung</i>, vol. 122,
    no. 1, Springer Fachmedien Wiesbaden GmbH, 2019, pp. 35–64, doi:<a href="https://doi.org/10.1365/s13291-019-00210-z">10.1365/s13291-019-00210-z</a>.
  short: J. Lankeit, M. Winkler, Jahresbericht Der Deutschen Mathematiker-Vereinigung
    122 (2019) 35–64.
date_created: 2025-12-19T10:52:04Z
date_updated: 2025-12-19T10:52:11Z
doi: 10.1365/s13291-019-00210-z
intvolume: '       122'
issue: '1'
language:
- iso: eng
page: 35-64
publication: Jahresbericht der Deutschen Mathematiker-Vereinigung
publication_identifier:
  issn:
  - 0012-0456
  - 1869-7135
publication_status: published
publisher: Springer Fachmedien Wiesbaden GmbH
status: public
title: Facing Low Regularity in Chemotaxis Systems
type: journal_article
user_id: '31496'
volume: 122
year: '2019'
...