---
_id: '31261'
abstract:
- lang: eng
text: "Abstract\r\n For a compact
Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector
bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal
M$, we give a precise description of those classical (Pollicott–Ruelle) resonant
states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the
Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal
M$. In particular, we show that they are isomorphically mapped by natural pushforwards
into generalized common eigenspaces of the algebra of invariant differential operators
$D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$
over $\\mathcal M$. As a consequence of this description, we obtain an exact band
structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions
on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau
}$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized
common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances
to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections
of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory
and Lie theory."
author:
- first_name: Benjamin
full_name: Küster, Benjamin
last_name: Küster
- first_name: Tobias
full_name: Weich, Tobias
last_name: Weich
citation:
ama: Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles
Over Locally Symmetric Spaces. International Mathematics Research Notices.
2021;2021(11):8225-8296. doi:10.1093/imrn/rnz068
apa: Küster, B., & Weich, T. (2021). Quantum-Classical Correspondence on Associated
Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research
Notices, 2021(11), 8225–8296. https://doi.org/10.1093/imrn/rnz068
bibtex: '@article{Küster_Weich_2021, title={Quantum-Classical Correspondence on
Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={10.1093/imrn/rnz068}, number={11},
journal={International Mathematics Research Notices}, publisher={Oxford University
Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2021}, pages={8225–8296}
}'
chicago: 'Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence
on Associated Vector Bundles Over Locally Symmetric Spaces.” International
Mathematics Research Notices 2021, no. 11 (2021): 8225–96. https://doi.org/10.1093/imrn/rnz068.'
ieee: 'B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector
Bundles Over Locally Symmetric Spaces,” International Mathematics Research
Notices, vol. 2021, no. 11, pp. 8225–8296, 2021, doi: 10.1093/imrn/rnz068.'
mla: Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated
Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research
Notices, vol. 2021, no. 11, Oxford University Press (OUP), 2021, pp. 8225–96,
doi:10.1093/imrn/rnz068.
short: B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021)
8225–8296.
date_created: 2022-05-17T12:00:36Z
date_updated: 2022-05-25T06:42:01Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: 10.1093/imrn/rnz068
external_id:
arxiv:
- '1710.04625'
intvolume: ' 2021'
issue: '11'
keyword:
- General Mathematics
language:
- iso: eng
page: 8225-8296
publication: International Mathematics Research Notices
publication_identifier:
issn:
- 1073-7928
- 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Quantum-Classical Correspondence on Associated Vector Bundles Over Locally
Symmetric Spaces
type: journal_article
user_id: '49178'
volume: 2021
year: '2021'
...
---
_id: '34818'
article_number: '101687'
article_type: original
author:
- first_name: Maximilian
full_name: Hanusch, Maximilian
id: '30905'
last_name: Hanusch
citation:
ama: Hanusch M. Symmetries of analytic curves. Differential Geometry and its
Applications. 2021;74. doi:10.1016/j.difgeo.2020.101687
apa: Hanusch, M. (2021). Symmetries of analytic curves. Differential Geometry
and Its Applications, 74, Article 101687. https://doi.org/10.1016/j.difgeo.2020.101687
bibtex: '@article{Hanusch_2021, title={Symmetries of analytic curves}, volume={74},
DOI={10.1016/j.difgeo.2020.101687},
number={101687}, journal={Differential Geometry and its Applications}, publisher={Elsevier
BV}, author={Hanusch, Maximilian}, year={2021} }'
chicago: Hanusch, Maximilian. “Symmetries of Analytic Curves.” Differential Geometry
and Its Applications 74 (2021). https://doi.org/10.1016/j.difgeo.2020.101687.
ieee: 'M. Hanusch, “Symmetries of analytic curves,” Differential Geometry and
its Applications, vol. 74, Art. no. 101687, 2021, doi: 10.1016/j.difgeo.2020.101687.'
mla: Hanusch, Maximilian. “Symmetries of Analytic Curves.” Differential Geometry
and Its Applications, vol. 74, 101687, Elsevier BV, 2021, doi:10.1016/j.difgeo.2020.101687.
short: M. Hanusch, Differential Geometry and Its Applications 74 (2021).
date_created: 2022-12-22T09:20:30Z
date_updated: 2023-01-09T18:07:26Z
department:
- _id: '93'
doi: 10.1016/j.difgeo.2020.101687
extern: '1'
intvolume: ' 74'
keyword:
- Geometry and Topology
- Analysis
language:
- iso: eng
publication: Differential Geometry and its Applications
publication_identifier:
issn:
- 0926-2245
publication_status: published
publisher: Elsevier BV
status: public
title: Symmetries of analytic curves
type: journal_article
user_id: '30905'
volume: 74
year: '2021'
...
---
_id: '31263'
author:
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Guillarmou C, Hilgert J, Weich T. High frequency limits for invariant Ruelle
densities. Annales Henri Lebesgue. 2021;4:81-119. doi:10.5802/ahl.67
apa: Guillarmou, C., Hilgert, J., & Weich, T. (2021). High frequency limits
for invariant Ruelle densities. Annales Henri Lebesgue, 4, 81–119.
https://doi.org/10.5802/ahl.67
bibtex: '@article{Guillarmou_Hilgert_Weich_2021, title={High frequency limits for
invariant Ruelle densities}, volume={4}, DOI={10.5802/ahl.67},
journal={Annales Henri Lebesgue}, publisher={Cellule MathDoc/CEDRAM}, author={Guillarmou,
Colin and Hilgert, Joachim and Weich, Tobias}, year={2021}, pages={81–119} }'
chicago: 'Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “High Frequency
Limits for Invariant Ruelle Densities.” Annales Henri Lebesgue 4 (2021):
81–119. https://doi.org/10.5802/ahl.67.'
ieee: 'C. Guillarmou, J. Hilgert, and T. Weich, “High frequency limits for invariant
Ruelle densities,” Annales Henri Lebesgue, vol. 4, pp. 81–119, 2021, doi:
10.5802/ahl.67.'
mla: Guillarmou, Colin, et al. “High Frequency Limits for Invariant Ruelle Densities.”
Annales Henri Lebesgue, vol. 4, Cellule MathDoc/CEDRAM, 2021, pp. 81–119,
doi:10.5802/ahl.67.
short: C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.
date_created: 2022-05-17T12:05:17Z
date_updated: 2024-02-19T06:27:43Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
doi: 10.5802/ahl.67
external_id:
arxiv:
- '1803.06717'
intvolume: ' 4'
language:
- iso: eng
page: 81-119
publication: Annales Henri Lebesgue
publication_identifier:
issn:
- 2644-9463
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: High frequency limits for invariant Ruelle densities
type: journal_article
user_id: '49063'
volume: 4
year: '2021'
...
---
_id: '36271'
author:
- first_name: Dominik
full_name: Brennecken, Dominik
id: '55911'
last_name: Brennecken
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: Lorenzo
full_name: Ciardo, Lorenzo
last_name: Ciardo
citation:
ama: Brennecken D, Hilgert J, Ciardo L. Algebraically Independent Generators for
the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). Journal of
Lie Theory. 2021;31(2):459--468. doi:10.48550/arXiv.2008.07479
apa: Brennecken, D., Hilgert, J., & Ciardo, L. (2021). Algebraically Independent
Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).
Journal of Lie Theory, 31(2), 459--468. https://doi.org/10.48550/arXiv.2008.07479
bibtex: '@article{Brennecken_Hilgert_Ciardo_2021, title={Algebraically Independent
Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)},
volume={31}, DOI={10.48550/arXiv.2008.07479},
number={2}, journal={Journal of Lie Theory}, publisher={Heldermann Verlag}, author={Brennecken,
Dominik and Hilgert, Joachim and Ciardo, Lorenzo}, year={2021}, pages={459--468}
}'
chicago: 'Brennecken, Dominik, Joachim Hilgert, and Lorenzo Ciardo. “Algebraically
Independent Generators for the Algebra of Invariant Differential Operators on
SLn(R)/SOn(R).” Journal of Lie Theory 31, no. 2 (2021): 459--468. https://doi.org/10.48550/arXiv.2008.07479.'
ieee: 'D. Brennecken, J. Hilgert, and L. Ciardo, “Algebraically Independent Generators
for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R),” Journal
of Lie Theory, vol. 31, no. 2, pp. 459--468, 2021, doi: 10.48550/arXiv.2008.07479.'
mla: Brennecken, Dominik, et al. “Algebraically Independent Generators for the Algebra
of Invariant Differential Operators on SLn(R)/SOn(R).” Journal of Lie Theory,
vol. 31, no. 2, Heldermann Verlag, 2021, pp. 459--468, doi:10.48550/arXiv.2008.07479.
short: D. Brennecken, J. Hilgert, L. Ciardo, Journal of Lie Theory 31 (2021) 459--468.
date_created: 2023-01-12T08:23:28Z
date_updated: 2024-02-19T06:27:09Z
department:
- _id: '555'
- _id: '91'
doi: 10.48550/arXiv.2008.07479
intvolume: ' 31'
issue: '2'
language:
- iso: eng
page: 459--468
publication: Journal of Lie Theory
publication_status: published
publisher: Heldermann Verlag
status: public
title: Algebraically Independent Generators for the Algebra of Invariant Differential
Operators on SLn(R)/SOn(R)
type: journal_article
user_id: '49063'
volume: 31
year: '2021'
...
---
_id: '51556'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: 'Hilgert J. Philip Ording: 99 Variations on a Proof. Princeton University Press
2019. Mathematische Semesterberichte. 2021;68:171–173. doi:10.1007/s00591-021-00295-7'
apa: 'Hilgert, J. (2021). Philip Ording: 99 Variations on a Proof. Princeton University
Press 2019. In Mathematische Semesterberichte (Vol. 68, pp. 171–173). https://doi.org/10.1007/s00591-021-00295-7'
bibtex: '@article{Hilgert_2021, title={Philip Ording: 99 Variations on a Proof.
Princeton University Press 2019}, volume={68}, DOI={10.1007/s00591-021-00295-7},
journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2021},
pages={171–173} }'
chicago: 'Hilgert, Joachim. “Philip Ording: 99 Variations on a Proof. Princeton
University Press 2019.” Mathematische Semesterberichte, 2021. https://doi.org/10.1007/s00591-021-00295-7.'
ieee: 'J. Hilgert, “Philip Ording: 99 Variations on a Proof. Princeton University
Press 2019,” Mathematische Semesterberichte, vol. 68. pp. 171–173, 2021,
doi: 10.1007/s00591-021-00295-7.'
mla: 'Hilgert, Joachim. “Philip Ording: 99 Variations on a Proof. Princeton University
Press 2019.” Mathematische Semesterberichte, vol. 68, 2021, pp. 171–173,
doi:10.1007/s00591-021-00295-7.'
short: J. Hilgert, Mathematische Semesterberichte 68 (2021) 171–173.
date_created: 2024-02-20T09:52:08Z
date_updated: 2024-02-20T10:03:43Z
department:
- _id: '91'
doi: 10.1007/s00591-021-00295-7
intvolume: ' 68'
language:
- iso: eng
page: 171–173
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Philip Ording: 99 Variations on a Proof. Princeton University Press 2019'
type: review
user_id: '49063'
volume: 68
year: '2021'
...
---
_id: '51555'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: 'Hilgert J. Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame
Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020. Mathematische
Semesterberichte. 2021;68:175–177. doi:10.1007/s00591-021-00296-6'
apa: 'Hilgert, J. (2021). Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch
– Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020.
In Mathematische Semesterberichte (Vol. 68, pp. 175–177). https://doi.org/10.1007/s00591-021-00296-6'
bibtex: '@article{Hilgert_2021, title={Georg Glaeser (Hrsg.): 77-mal Mathematik
für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer
Spektrum 2020}, volume={68}, DOI={10.1007/s00591-021-00296-6},
journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2021},
pages={175–177} }'
chicago: 'Hilgert, Joachim. “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch
– Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020.”
Mathematische Semesterberichte, 2021. https://doi.org/10.1007/s00591-021-00296-6.'
ieee: 'J. Hilgert, “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch –
Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020,”
Mathematische Semesterberichte, vol. 68. pp. 175–177, 2021, doi: 10.1007/s00591-021-00296-6.'
mla: 'Hilgert, Joachim. “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch
– Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020.”
Mathematische Semesterberichte, vol. 68, 2021, pp. 175–177, doi:10.1007/s00591-021-00296-6.'
short: J. Hilgert, Mathematische Semesterberichte 68 (2021) 175–177.
date_created: 2024-02-20T09:50:31Z
date_updated: 2024-02-20T10:14:56Z
department:
- _id: '91'
doi: 10.1007/s00591-021-00296-6
intvolume: ' 68'
language:
- iso: ger
page: 175–177
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame
Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020'
type: review
user_id: '49063'
volume: 68
year: '2021'
...
---
_id: '32006'
author:
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
- first_name: Benjamin
full_name: Küster, Benjamin
last_name: Küster
citation:
ama: Guillarmou C, Küster B. Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.
Annales Henri Poincaré. 2021;22(11):3565-3617. doi:10.1007/s00023-021-01068-7
apa: Guillarmou, C., & Küster, B. (2021). Spectral Theory of the Frame Flow
on Hyperbolic 3-Manifolds. Annales Henri Poincaré, 22(11), 3565–3617.
https://doi.org/10.1007/s00023-021-01068-7
bibtex: '@article{Guillarmou_Küster_2021, title={Spectral Theory of the Frame Flow
on Hyperbolic 3-Manifolds}, volume={22}, DOI={10.1007/s00023-021-01068-7},
number={11}, journal={Annales Henri Poincaré}, publisher={Springer Science and
Business Media LLC}, author={Guillarmou, Colin and Küster, Benjamin}, year={2021},
pages={3565–3617} }'
chicago: 'Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame
Flow on Hyperbolic 3-Manifolds.” Annales Henri Poincaré 22, no. 11 (2021):
3565–3617. https://doi.org/10.1007/s00023-021-01068-7.'
ieee: 'C. Guillarmou and B. Küster, “Spectral Theory of the Frame Flow on Hyperbolic
3-Manifolds,” Annales Henri Poincaré, vol. 22, no. 11, pp. 3565–3617, 2021,
doi: 10.1007/s00023-021-01068-7.'
mla: Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow
on Hyperbolic 3-Manifolds.” Annales Henri Poincaré, vol. 22, no. 11, Springer
Science and Business Media LLC, 2021, pp. 3565–617, doi:10.1007/s00023-021-01068-7.
short: C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617.
date_created: 2022-06-20T08:37:52Z
date_updated: 2024-04-11T12:39:23Z
department:
- _id: '548'
doi: 10.1007/s00023-021-01068-7
intvolume: ' 22'
issue: '11'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 3565-3617
publication: Annales Henri Poincaré
publication_identifier:
issn:
- 1424-0637
- 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds
type: journal_article
user_id: '70575'
volume: 22
year: '2021'
...
---
_id: '35702'
abstract:
- lang: eng
text: AbstractMathematics Learning Support Centres
are becoming more and more common in higher education both internationally and
in Germany. Whereas it is clear that their quality largely depends on a functioning
interaction in consultations, little is known about how such consultations proceed
in detail. On the basis of models from the literature and recorded support sessions
(N = 36), we constructed a process model that divides consultations into four
ideal–typical phases. In the individual consultations, forward or backward leaps
occur, but overall the model seems to describe the data well. A high intercoder
reliability shows that it can be applied consistently on real data by different
researchers. An analysis of the consultations between students and tutors shows
that both mainly work on past attempts or thoughts of the students to solve the
exercise or problems and on concrete strategies to solve a problem within the
session. In contrast, very little time is dedicated to summarizing and reflecting
the solution. The data allows for a more in-depth discussion of what constitutes
quality in advising processes and how it might be further explored. Practically,
the model may structure support sessions and help in focussing on different goals
in different phases.
author:
- first_name: Mirko
full_name: Schürmann, Mirko
id: '59707'
last_name: Schürmann
orcid: 0000-0003-2646-085X
- first_name: Anja
full_name: Panse, Anja
last_name: Panse
- first_name: Zain
full_name: Shaikh, Zain
last_name: Shaikh
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Niclas
full_name: Schaper, Niclas
last_name: Schaper
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: Schürmann M, Panse A, Shaikh Z, et al. Consultation Phases in Mathematics Learning
and Support Centres. International Journal of Research in Undergraduate Mathematics
Education. 2021;8(1):94-120. doi:10.1007/s40753-021-00154-9
apa: Schürmann, M., Panse, A., Shaikh, Z., Biehler, R., Schaper, N., Liebendörfer,
M., & Hilgert, J. (2021). Consultation Phases in Mathematics Learning and
Support Centres. International Journal of Research in Undergraduate Mathematics
Education, 8(1), 94–120. https://doi.org/10.1007/s40753-021-00154-9
bibtex: '@article{Schürmann_Panse_Shaikh_Biehler_Schaper_Liebendörfer_Hilgert_2021,
title={Consultation Phases in Mathematics Learning and Support Centres}, volume={8},
DOI={10.1007/s40753-021-00154-9},
number={1}, journal={International Journal of Research in Undergraduate Mathematics
Education}, publisher={Springer Science and Business Media LLC}, author={Schürmann,
Mirko and Panse, Anja and Shaikh, Zain and Biehler, Rolf and Schaper, Niclas and
Liebendörfer, Michael and Hilgert, Joachim}, year={2021}, pages={94–120} }'
chicago: 'Schürmann, Mirko, Anja Panse, Zain Shaikh, Rolf Biehler, Niclas Schaper,
Michael Liebendörfer, and Joachim Hilgert. “Consultation Phases in Mathematics
Learning and Support Centres.” International Journal of Research in Undergraduate
Mathematics Education 8, no. 1 (2021): 94–120. https://doi.org/10.1007/s40753-021-00154-9.'
ieee: 'M. Schürmann et al., “Consultation Phases in Mathematics Learning
and Support Centres,” International Journal of Research in Undergraduate Mathematics
Education, vol. 8, no. 1, pp. 94–120, 2021, doi: 10.1007/s40753-021-00154-9.'
mla: Schürmann, Mirko, et al. “Consultation Phases in Mathematics Learning and Support
Centres.” International Journal of Research in Undergraduate Mathematics Education,
vol. 8, no. 1, Springer Science and Business Media LLC, 2021, pp. 94–120, doi:10.1007/s40753-021-00154-9.
short: M. Schürmann, A. Panse, Z. Shaikh, R. Biehler, N. Schaper, M. Liebendörfer,
J. Hilgert, International Journal of Research in Undergraduate Mathematics Education
8 (2021) 94–120.
date_created: 2023-01-10T09:09:23Z
date_updated: 2024-04-18T10:09:08Z
department:
- _id: '363'
- _id: '423'
- _id: '91'
- _id: '625'
doi: 10.1007/s40753-021-00154-9
intvolume: ' 8'
issue: '1'
keyword:
- Education
- Mathematics (miscellaneous)
language:
- iso: eng
page: 94-120
publication: International Journal of Research in Undergraduate Mathematics Education
publication_identifier:
issn:
- 2198-9745
- 2198-9753
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Consultation Phases in Mathematics Learning and Support Centres
type: journal_article
user_id: '37888'
volume: 8
year: '2021'
...
---
_id: '51493'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: Ingrid
full_name: Hilgert, Ingrid
last_name: Hilgert
citation:
ama: Hilgert J, Hilgert I. Mathematik - Ein Reiseführer 2. Auflage. Springer
Spektrum; 2021.
apa: Hilgert, J., & Hilgert, I. (2021). Mathematik - Ein Reiseführer 2. Auflage.
Springer Spektrum.
bibtex: '@book{Hilgert_Hilgert_2021, title={Mathematik - Ein Reiseführer 2. Auflage},
publisher={Springer Spektrum}, author={Hilgert, Joachim and Hilgert, Ingrid},
year={2021} }'
chicago: Hilgert, Joachim, and Ingrid Hilgert. Mathematik - Ein Reiseführer 2.
Auflage. Springer Spektrum, 2021.
ieee: J. Hilgert and I. Hilgert, Mathematik - Ein Reiseführer 2. Auflage.
Springer Spektrum, 2021.
mla: Hilgert, Joachim, and Ingrid Hilgert. Mathematik - Ein Reiseführer 2. Auflage.
Springer Spektrum, 2021.
short: J. Hilgert, I. Hilgert, Mathematik - Ein Reiseführer 2. Auflage, Springer
Spektrum, 2021.
date_created: 2024-02-19T10:21:25Z
date_updated: 2024-08-08T07:49:11Z
department:
- _id: '91'
language:
- iso: ger
publication_status: published
publisher: Springer Spektrum
status: public
title: Mathematik - Ein Reiseführer 2. Auflage
type: book
user_id: '220'
year: '2021'
...
---
_id: '35615'
article_number: '72'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Suppressing blow-up by gradient-dependent flux limitation in a planar
Keller-Segel-Navier-Stokes system. Zeitschrift für Angewandte Mathematik und
Physik. 2021;72.
apa: Winkler, M. (2021). Suppressing blow-up by gradient-dependent flux limitation
in a planar Keller-Segel-Navier-Stokes system. Zeitschrift Für Angewandte Mathematik
Und Physik, 72, Article 72.
bibtex: '@article{Winkler_2021, title={Suppressing blow-up by gradient-dependent
flux limitation in a planar Keller-Segel-Navier-Stokes system.}, volume={72},
number={72}, journal={Zeitschrift für Angewandte Mathematik und Physik}, author={Winkler,
Michael}, year={2021} }'
chicago: Winkler, Michael. “Suppressing Blow-up by Gradient-Dependent Flux Limitation
in a Planar Keller-Segel-Navier-Stokes System.” Zeitschrift Für Angewandte
Mathematik Und Physik 72 (2021).
ieee: M. Winkler, “Suppressing blow-up by gradient-dependent flux limitation in
a planar Keller-Segel-Navier-Stokes system.,” Zeitschrift für Angewandte Mathematik
und Physik, vol. 72, Art. no. 72, 2021.
mla: Winkler, Michael. “Suppressing Blow-up by Gradient-Dependent Flux Limitation
in a Planar Keller-Segel-Navier-Stokes System.” Zeitschrift Für Angewandte
Mathematik Und Physik, vol. 72, 72, 2021.
short: M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).
date_created: 2023-01-09T18:16:56Z
date_updated: 2023-01-20T13:14:53Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 72'
language:
- iso: eng
publication: Zeitschrift für Angewandte Mathematik und Physik
status: public
title: Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes
system.
type: journal_article
user_id: '15645'
volume: 72
year: '2021'
...
---
_id: '35614'
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? International Mathematics Research Notices.
2021;2021:8106-8152.
apa: Winkler, M. (2021). Can rotational fluxes impede the tendency toward spatial
homogeneity in nutrient taxis (-Stokes) systems? International Mathematics
Research Notices, 2021, 8106–8152.
bibtex: '@article{Winkler_2021, title={Can rotational fluxes impede the tendency
toward spatial homogeneity in nutrient taxis (-Stokes) systems?}, volume={2021},
journal={International Mathematics Research Notices}, author={Winkler, Michael},
year={2021}, pages={8106–8152} }'
chicago: 'Winkler, Michael. “Can Rotational Fluxes Impede the Tendency toward Spatial
Homogeneity in Nutrient Taxis (-Stokes) Systems?” International Mathematics
Research Notices 2021 (2021): 8106–52.'
ieee: M. Winkler, “Can rotational fluxes impede the tendency toward spatial homogeneity
in nutrient taxis (-Stokes) systems?,” International Mathematics Research Notices,
vol. 2021, pp. 8106–8152, 2021.
mla: Winkler, Michael. “Can Rotational Fluxes Impede the Tendency toward Spatial
Homogeneity in Nutrient Taxis (-Stokes) Systems?” International Mathematics
Research Notices, vol. 2021, 2021, pp. 8106–52.
short: M. Winkler, International Mathematics Research Notices 2021 (2021) 8106–8152.
date_created: 2023-01-09T18:14:20Z
date_updated: 2023-01-20T13:14:58Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 2021'
language:
- iso: eng
page: 8106-8152
publication: International Mathematics Research Notices
status: public
title: Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient
taxis (-Stokes) systems?
type: journal_article
user_id: '15645'
volume: 2021
year: '2021'
...
---
_id: '35617'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Boundedness in a three-dimensional Keller-Segel-Stokes system with
subcritical sensitivity. Applied Mathematics Letters. 2021;112:106785.
apa: Winkler, M. (2021). Boundedness in a three-dimensional Keller-Segel-Stokes
system with subcritical sensitivity. Applied Mathematics Letters, 112,
106785.
bibtex: '@article{Winkler_2021, title={Boundedness in a three-dimensional Keller-Segel-Stokes
system with subcritical sensitivity.}, volume={112}, journal={Applied Mathematics
Letters}, author={Winkler, Michael}, year={2021}, pages={106785} }'
chicago: 'Winkler, Michael. “Boundedness in a Three-Dimensional Keller-Segel-Stokes
System with Subcritical Sensitivity.” Applied Mathematics Letters 112 (2021):
106785.'
ieee: M. Winkler, “Boundedness in a three-dimensional Keller-Segel-Stokes system
with subcritical sensitivity.,” Applied Mathematics Letters, vol. 112,
p. 106785, 2021.
mla: Winkler, Michael. “Boundedness in a Three-Dimensional Keller-Segel-Stokes System
with Subcritical Sensitivity.” Applied Mathematics Letters, vol. 112, 2021,
p. 106785.
short: M. Winkler, Applied Mathematics Letters 112 (2021) 106785.
date_created: 2023-01-09T18:21:39Z
date_updated: 2023-01-20T13:14:48Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 112'
language:
- iso: eng
page: '106785'
publication: Applied Mathematics Letters
status: public
title: Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical
sensitivity.
type: journal_article
user_id: '15645'
volume: 112
year: '2021'
...
---
_id: '35613'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Does spatial homogeneity ultimately prevail in nutrient taxis systems?
A paradigm for structure support by rapid diffusion decay in an autonomous parabolic
flow. Transactions of the American Mathematical Society. 2021;374:219-268.
apa: Winkler, M. (2021). Does spatial homogeneity ultimately prevail in nutrient
taxis systems? A paradigm for structure support by rapid diffusion decay in an
autonomous parabolic flow. Transactions of the American Mathematical Society,
374, 219–268.
bibtex: '@article{Winkler_2021, title={Does spatial homogeneity ultimately prevail
in nutrient taxis systems? A paradigm for structure support by rapid diffusion
decay in an autonomous parabolic flow.}, volume={374}, journal={Transactions of
the American Mathematical Society}, author={Winkler, Michael}, year={2021}, pages={219–268}
}'
chicago: 'Winkler, Michael. “Does Spatial Homogeneity Ultimately Prevail in Nutrient
Taxis Systems? A Paradigm for Structure Support by Rapid Diffusion Decay in an
Autonomous Parabolic Flow.” Transactions of the American Mathematical Society
374 (2021): 219–68.'
ieee: M. Winkler, “Does spatial homogeneity ultimately prevail in nutrient taxis
systems? A paradigm for structure support by rapid diffusion decay in an autonomous
parabolic flow.,” Transactions of the American Mathematical Society, vol.
374, pp. 219–268, 2021.
mla: Winkler, Michael. “Does Spatial Homogeneity Ultimately Prevail in Nutrient
Taxis Systems? A Paradigm for Structure Support by Rapid Diffusion Decay in an
Autonomous Parabolic Flow.” Transactions of the American Mathematical Society,
vol. 374, 2021, pp. 219–68.
short: M. Winkler, Transactions of the American Mathematical Society 374 (2021)
219–268.
date_created: 2023-01-09T18:11:15Z
date_updated: 2023-01-20T13:15:03Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 374'
language:
- iso: eng
page: 219-268
publication: Transactions of the American Mathematical Society
status: public
title: Does spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm
for structure support by rapid diffusion decay in an autonomous parabolic flow.
type: journal_article
user_id: '15645'
volume: 374
year: '2021'
...
---
_id: '37659'
author:
- first_name: Margit
full_name: Rösler, Margit
id: '37390'
last_name: Rösler
- first_name: Michael
full_name: Voit, Michael
last_name: Voit
citation:
ama: Rösler M, Voit M. Positive intertwiners for Bessel functions of type B. Proceedings
of the American Mathematical Society. 2021;149(3):1151-1163. doi:10.1090/proc/15312
apa: Rösler, M., & Voit, M. (2021). Positive intertwiners for Bessel functions
of type B. Proceedings of the American Mathematical Society, 149(3),
1151–1163. https://doi.org/10.1090/proc/15312
bibtex: '@article{Rösler_Voit_2021, title={Positive intertwiners for Bessel functions
of type B}, volume={149}, DOI={10.1090/proc/15312},
number={3}, journal={Proceedings of the American Mathematical Society}, publisher={American
Mathematical Society (AMS)}, author={Rösler, Margit and Voit, Michael}, year={2021},
pages={1151–1163} }'
chicago: 'Rösler, Margit, and Michael Voit. “Positive Intertwiners for Bessel Functions
of Type B.” Proceedings of the American Mathematical Society 149, no. 3
(2021): 1151–63. https://doi.org/10.1090/proc/15312.'
ieee: 'M. Rösler and M. Voit, “Positive intertwiners for Bessel functions of type
B,” Proceedings of the American Mathematical Society, vol. 149, no. 3,
pp. 1151–1163, 2021, doi: 10.1090/proc/15312.'
mla: Rösler, Margit, and Michael Voit. “Positive Intertwiners for Bessel Functions
of Type B.” Proceedings of the American Mathematical Society, vol. 149,
no. 3, American Mathematical Society (AMS), 2021, pp. 1151–63, doi:10.1090/proc/15312.
short: M. Rösler, M. Voit, Proceedings of the American Mathematical Society 149
(2021) 1151–1163.
date_created: 2023-01-20T09:22:12Z
date_updated: 2023-01-24T22:16:16Z
department:
- _id: '555'
doi: 10.1090/proc/15312
intvolume: ' 149'
issue: '3'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 1151-1163
publication: Proceedings of the American Mathematical Society
publication_identifier:
issn:
- 0002-9939
- 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Positive intertwiners for Bessel functions of type B
type: journal_article
user_id: '37390'
volume: 149
year: '2021'
...
---
_id: '35603'
article_number: '109069'
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 fully cross-diffusive two-component evolution system:
Existence and qualitative analysis via entropy-consistent thin-film-type approximation.
Journal of Functional Analysis. 2021;281.'
apa: 'Tao, Y., & Winkler, M. (2021). A fully cross-diffusive two-component evolution
system: Existence and qualitative analysis via entropy-consistent thin-film-type
approximation. Journal of Functional Analysis, 281, Article 109069.'
bibtex: '@article{Tao_Winkler_2021, title={A fully cross-diffusive two-component
evolution system: Existence and qualitative analysis via entropy-consistent thin-film-type
approximation.}, volume={281}, number={109069}, journal={Journal of Functional
Analysis}, author={Tao, Youshan and Winkler, Michael}, year={2021} }'
chicago: 'Tao, Youshan, and Michael Winkler. “A Fully Cross-Diffusive Two-Component
Evolution System: Existence and Qualitative Analysis via Entropy-Consistent Thin-Film-Type
Approximation.” Journal of Functional Analysis 281 (2021).'
ieee: 'Y. Tao and M. Winkler, “A fully cross-diffusive two-component evolution system:
Existence and qualitative analysis via entropy-consistent thin-film-type approximation.,”
Journal of Functional Analysis, vol. 281, Art. no. 109069, 2021.'
mla: 'Tao, Youshan, and Michael Winkler. “A Fully Cross-Diffusive Two-Component
Evolution System: Existence and Qualitative Analysis via Entropy-Consistent Thin-Film-Type
Approximation.” Journal of Functional Analysis, vol. 281, 109069, 2021.'
short: Y. Tao, M. Winkler, Journal of Functional Analysis 281 (2021).
date_created: 2023-01-09T17:28:08Z
date_updated: 2023-02-01T10:18:18Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 281'
language:
- iso: eng
publication: Journal of Functional Analysis
status: public
title: 'A fully cross-diffusive two-component evolution system: Existence and qualitative
analysis via entropy-consistent thin-film-type approximation.'
type: journal_article
user_id: '15645'
volume: 281
year: '2021'
...
---
_id: '35612'
author:
- first_name: Yulan
full_name: Wang, Yulan
last_name: Wang
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
- first_name: Zhaoyin
full_name: Xiang, Zhaoyin
last_name: Xiang
citation:
ama: Wang Y, Winkler M, Xiang Z. Immediate regularization of measure-type population
densities in a two-dimensional chemotaxis system with signal consumption. Science
China Mathematics. 2021;64:725-746.
apa: Wang, Y., Winkler, M., & Xiang, Z. (2021). Immediate regularization of
measure-type population densities in a two-dimensional chemotaxis system with
signal consumption. Science China Mathematics, 64, 725–746.
bibtex: '@article{Wang_Winkler_Xiang_2021, title={Immediate regularization of measure-type
population densities in a two-dimensional chemotaxis system with signal consumption.},
volume={64}, journal={Science China Mathematics}, author={Wang, Yulan and Winkler,
Michael and Xiang, Zhaoyin}, year={2021}, pages={725–746} }'
chicago: 'Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “Immediate Regularization
of Measure-Type Population Densities in a Two-Dimensional Chemotaxis System with
Signal Consumption.” Science China Mathematics 64 (2021): 725–46.'
ieee: Y. Wang, M. Winkler, and Z. Xiang, “Immediate regularization of measure-type
population densities in a two-dimensional chemotaxis system with signal consumption.,”
Science China Mathematics, vol. 64, pp. 725–746, 2021.
mla: Wang, Yulan, et al. “Immediate Regularization of Measure-Type Population Densities
in a Two-Dimensional Chemotaxis System with Signal Consumption.” Science China
Mathematics, vol. 64, 2021, pp. 725–46.
short: Y. Wang, M. Winkler, Z. Xiang, Science China Mathematics 64 (2021) 725–746.
date_created: 2023-01-09T18:06:08Z
date_updated: 2023-02-01T10:22:22Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 64'
language:
- iso: eng
page: 725-746
publication: Science China Mathematics
status: public
title: Immediate regularization of measure-type population densities in a two-dimensional
chemotaxis system with signal consumption.
type: journal_article
user_id: '15645'
volume: 64
year: '2021'
...
---
_id: '35605'
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 solutions in a two-dimensional cross-diffusion
system modeling propagation of urban crime. Communications in Mathematical
Sciences. 2021;19:829-849.
apa: Tao, Y., & Winkler, M. (2021). Global smooth solutions in a two-dimensional
cross-diffusion system modeling propagation of urban crime. Communications
in Mathematical Sciences, 19, 829–849.
bibtex: '@article{Tao_Winkler_2021, title={Global smooth solutions in a two-dimensional
cross-diffusion system modeling propagation of urban crime.}, volume={19}, journal={Communications
in Mathematical Sciences}, author={Tao, Youshan and Winkler, Michael}, year={2021},
pages={829–849} }'
chicago: 'Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Two-Dimensional
Cross-Diffusion System Modeling Propagation of Urban Crime.” Communications
in Mathematical Sciences 19 (2021): 829–49.'
ieee: Y. Tao and M. Winkler, “Global smooth solutions in a two-dimensional cross-diffusion
system modeling propagation of urban crime.,” Communications in Mathematical
Sciences, vol. 19, pp. 829–849, 2021.
mla: Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Two-Dimensional
Cross-Diffusion System Modeling Propagation of Urban Crime.” Communications
in Mathematical Sciences, vol. 19, 2021, pp. 829–49.
short: Y. Tao, M. Winkler, Communications in Mathematical Sciences 19 (2021) 829–849.
date_created: 2023-01-09T17:32:36Z
date_updated: 2023-02-01T10:23:03Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 19'
language:
- iso: eng
page: 829-849
publication: Communications in Mathematical Sciences
status: public
title: Global smooth solutions in a two-dimensional cross-diffusion system modeling
propagation of urban crime.
type: journal_article
user_id: '15645'
volume: 19
year: '2021'
...
---
_id: '35610'
author:
- first_name: Yulan
full_name: Wang, Yulan
last_name: Wang
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
- first_name: Zhaoyin
full_name: Xiang, Zhaoyin
last_name: Xiang
citation:
ama: Wang Y, Winkler M, Xiang Z. Local energy estimates and global solvability in
a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.
Communications in Partial Differential Equations. 2021;46:1058-1091.
apa: Wang, Y., Winkler, M., & Xiang, Z. (2021). Local energy estimates and global
solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal
on the boundary. Communications in Partial Differential Equations, 46,
1058–1091.
bibtex: '@article{Wang_Winkler_Xiang_2021, title={Local energy estimates and global
solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal
on the boundary.}, volume={46}, journal={Communications in Partial Differential
Equations}, author={Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}, year={2021},
pages={1058–1091} }'
chicago: 'Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “Local Energy Estimates
and Global Solvability in a Threee-Dimensional Chemotaxis-Fluid System with Prescribed
Signal on the Boundary.” Communications in Partial Differential Equations
46 (2021): 1058–91.'
ieee: Y. Wang, M. Winkler, and Z. Xiang, “Local energy estimates and global solvability
in a threee-dimensional chemotaxis-fluid system with prescribed signal on the
boundary.,” Communications in Partial Differential Equations, vol. 46,
pp. 1058–1091, 2021.
mla: Wang, Yulan, et al. “Local Energy Estimates and Global Solvability in a Threee-Dimensional
Chemotaxis-Fluid System with Prescribed Signal on the Boundary.” Communications
in Partial Differential Equations, vol. 46, 2021, pp. 1058–91.
short: Y. Wang, M. Winkler, Z. Xiang, Communications in Partial Differential Equations
46 (2021) 1058–1091.
date_created: 2023-01-09T18:00:41Z
date_updated: 2023-02-01T10:25:34Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 46'
language:
- iso: eng
page: 1058-1091
publication: Communications in Partial Differential Equations
status: public
title: Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid
system with prescribed signal on the boundary.
type: journal_article
user_id: '15645'
volume: 46
year: '2021'
...
---
_id: '35611'
author:
- first_name: Yulan
full_name: Wang, Yulan
last_name: Wang
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
- first_name: Zhaoyin
full_name: Xiang, Zhaoyin
last_name: Xiang
citation:
ama: Wang Y, Winkler M, Xiang Z. Global solvability in a threee-dimensional Keller-Segel.Stokes
system involving arbitrary superlinear logistic degradation. Advances in Nonlinear
Analysis. 2021;10:707-731.
apa: Wang, Y., Winkler, M., & Xiang, Z. (2021). Global solvability in a threee-dimensional
Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation.
Advances in Nonlinear Analysis, 10, 707–731.
bibtex: '@article{Wang_Winkler_Xiang_2021, title={Global solvability in a threee-dimensional
Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation},
volume={10}, journal={Advances in Nonlinear Analysis}, author={Wang, Yulan and
Winkler, Michael and Xiang, Zhaoyin}, year={2021}, pages={707–731} }'
chicago: 'Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “Global Solvability in
a Threee-Dimensional Keller-Segel.Stokes System Involving Arbitrary Superlinear
Logistic Degradation.” Advances in Nonlinear Analysis 10 (2021): 707–31.'
ieee: Y. Wang, M. Winkler, and Z. Xiang, “Global solvability in a threee-dimensional
Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation,”
Advances in Nonlinear Analysis, vol. 10, pp. 707–731, 2021.
mla: Wang, Yulan, et al. “Global Solvability in a Threee-Dimensional Keller-Segel.Stokes
System Involving Arbitrary Superlinear Logistic Degradation.” Advances in Nonlinear
Analysis, vol. 10, 2021, pp. 707–31.
short: Y. Wang, M. Winkler, Z. Xiang, Advances in Nonlinear Analysis 10 (2021) 707–731.
date_created: 2023-01-09T18:03:45Z
date_updated: 2023-02-01T10:27:17Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
intvolume: ' 10'
language:
- iso: eng
page: 707-731
publication: Advances in Nonlinear Analysis
status: public
title: Global solvability in a threee-dimensional Keller-Segel.Stokes system involving
arbitrary superlinear logistic degradation
type: journal_article
user_id: '15645'
volume: 10
year: '2021'
...
---
_id: '34673'
article_number: '96'
author:
- first_name: Tobias
full_name: Black, Tobias
id: '23686'
last_name: Black
orcid: 0000-0001-9963-0800
- first_name: Mario
full_name: Fuest, Mario
last_name: Fuest
- first_name: Johannes
full_name: Lankeit, Johannes
last_name: Lankeit
citation:
ama: Black T, Fuest M, Lankeit J. Relaxed parameter conditions for chemotactic collapse
in logistic-type parabolic–elliptic Keller–Segel systems. Zeitschrift für angewandte
Mathematik und Physik. 2021;72(3). doi:10.1007/s00033-021-01524-8
apa: Black, T., Fuest, M., & Lankeit, J. (2021). Relaxed parameter conditions
for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems.
Zeitschrift Für Angewandte Mathematik Und Physik, 72(3), Article
96. https://doi.org/10.1007/s00033-021-01524-8
bibtex: '@article{Black_Fuest_Lankeit_2021, title={Relaxed parameter conditions
for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems},
volume={72}, DOI={10.1007/s00033-021-01524-8},
number={396}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
Science and Business Media LLC}, author={Black, Tobias and Fuest, Mario and Lankeit,
Johannes}, year={2021} }'
chicago: Black, Tobias, Mario Fuest, and Johannes Lankeit. “Relaxed Parameter Conditions
for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.”
Zeitschrift Für Angewandte Mathematik Und Physik 72, no. 3 (2021). https://doi.org/10.1007/s00033-021-01524-8.
ieee: 'T. Black, M. Fuest, and J. Lankeit, “Relaxed parameter conditions for chemotactic
collapse in logistic-type parabolic–elliptic Keller–Segel systems,” Zeitschrift
für angewandte Mathematik und Physik, vol. 72, no. 3, Art. no. 96, 2021, doi:
10.1007/s00033-021-01524-8.'
mla: Black, Tobias, et al. “Relaxed Parameter Conditions for Chemotactic Collapse
in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” Zeitschrift Für
Angewandte Mathematik Und Physik, vol. 72, no. 3, 96, Springer Science and
Business Media LLC, 2021, doi:10.1007/s00033-021-01524-8.
short: T. Black, M. Fuest, J. Lankeit, Zeitschrift Für Angewandte Mathematik Und
Physik 72 (2021).
date_created: 2022-12-21T09:48:36Z
date_updated: 2023-07-10T11:39:23Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1007/s00033-021-01524-8
intvolume: ' 72'
issue: '3'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
publication: Zeitschrift für angewandte Mathematik und Physik
publication_identifier:
issn:
- 0044-2275
- 1420-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic
Keller–Segel systems
type: journal_article
user_id: '23686'
volume: 72
year: '2021'
...