---
_id: '63250'
abstract:
- lang: eng
text: "Abstract\r\n \r\n An
initial-boundary value problem for\r\n \r\n
\ \r\n $$\\begin{aligned}
\\left\\{ \\begin{array}{ll}u_{tt} = \\big (\\gamma (\\Theta ) u_{xt}\\big )_x
+ au_{xx} - \\big (f(\\Theta )\\big )_x, \\qquad & x\\in \\Omega , \\ t>0,
\\\\[1mm] \\Theta _t = \\Theta _{xx} + \\gamma (\\Theta ) u_{xt}^2 - f(\\Theta
) u_{xt}, \\qquad & x\\in \\Omega , \\ t>0, \\end{array} \\right. \\end{aligned}$$\r\n
\ \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n u\r\n
\ \r\n tt\r\n
\ \r\n \r\n
\ =\r\n \r\n
\ (\r\n \r\n
\ γ\r\n \r\n
\ (\r\n Θ\r\n
\ )\r\n \r\n
\ \r\n u\r\n
\ \r\n xt\r\n
\ \r\n \r\n
\ \r\n \r\n
\ )\r\n \r\n
\ x\r\n \r\n
\ +\r\n a\r\n
\ \r\n u\r\n
\ \r\n xx\r\n
\ \r\n \r\n
\ -\r\n \r\n
\ (\r\n \r\n
\ f\r\n \r\n
\ (\r\n Θ\r\n
\ )\r\n \r\n
\ \r\n \r\n
\ )\r\n \r\n
\ x\r\n \r\n
\ ,\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ x\r\n ∈\r\n
\ Ω\r\n ,\r\n
\ \r\n t\r\n
\ >\r\n 0\r\n
\ ,\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n [\r\n
\ 1\r\n m\r\n
\ m\r\n ]\r\n
\ \r\n \r\n
\ Θ\r\n t\r\n
\ \r\n =\r\n
\ \r\n Θ\r\n
\ \r\n xx\r\n
\ \r\n \r\n
\ +\r\n γ\r\n
\ \r\n (\r\n
\ Θ\r\n )\r\n
\ \r\n \r\n
\ u\r\n \r\n
\ xt\r\n \r\n
\ 2\r\n \r\n
\ -\r\n f\r\n
\ \r\n (\r\n
\ Θ\r\n )\r\n
\ \r\n \r\n
\ u\r\n \r\n
\ xt\r\n \r\n
\ \r\n ,\r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n x\r\n
\ ∈\r\n Ω\r\n
\ ,\r\n \r\n
\ t\r\n >\r\n
\ 0\r\n ,\r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n is considered
in an open bounded real interval\r\n \r\n
\ \r\n $$\\Omega
$$\r\n \r\n
\ Ω\r\n \r\n
\ \r\n \r\n
\ . Under the assumption that\r\n \r\n
\ \r\n $$\\gamma
\\in C^0([0,\\infty ))$$\r\n \r\n \r\n
\ γ\r\n ∈\r\n
\ \r\n C\r\n
\ 0\r\n \r\n
\ \r\n (\r\n
\ \r\n [\r\n
\ 0\r\n ,\r\n
\ ∞\r\n )\r\n
\ \r\n )\r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n and\r\n \r\n
\ \r\n $$f\\in
C^0([0,\\infty ))$$\r\n \r\n
\ \r\n f\r\n
\ ∈\r\n \r\n
\ C\r\n 0\r\n
\ \r\n \r\n
\ (\r\n \r\n
\ [\r\n 0\r\n
\ ,\r\n ∞\r\n
\ )\r\n \r\n
\ )\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ are such that\r\n \r\n
\ \r\n $$f(0)=0$$\r\n
\ \r\n
\ \r\n f\r\n
\ (\r\n 0\r\n
\ )\r\n =\r\n
\ 0\r\n \r\n
\ \r\n \r\n
\ \r\n , and\r\n \r\n
\ \r\n $$k_\\gamma
\\le \\gamma \\le K_\\gamma $$\r\n \r\n \r\n
\ \r\n k\r\n
\ γ\r\n \r\n
\ ≤\r\n γ\r\n
\ ≤\r\n \r\n
\ K\r\n γ\r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n as well as\r\n
\ \r\n \r\n
\ $$\\begin{aligned} |f(\\xi )| \\le K_f
\\cdot (\\xi +1)^\\alpha \\qquad \\hbox {for all } \\xi \\ge 0 \\end{aligned}$$\r\n
\ \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ |\r\n f\r\n
\ \r\n (\r\n
\ ξ\r\n )\r\n
\ \r\n |\r\n
\ \r\n ≤\r\n
\ \r\n K\r\n
\ f\r\n \r\n
\ ·\r\n \r\n
\ \r\n (\r\n
\ ξ\r\n +\r\n
\ 1\r\n )\r\n
\ \r\n α\r\n
\ \r\n \r\n
\ for all\r\n \r\n
\ ξ\r\n ≥\r\n
\ 0\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n with some\r\n
\ \r\n \r\n
\ $$k_\\gamma>0, K_\\gamma>0, K_f>0$$\r\n
\ \r\n
\ \r\n \r\n
\ k\r\n γ\r\n
\ \r\n >\r\n
\ 0\r\n ,\r\n
\ \r\n K\r\n
\ γ\r\n \r\n
\ >\r\n 0\r\n
\ ,\r\n \r\n
\ K\r\n f\r\n
\ \r\n >\r\n
\ 0\r\n \r\n
\ \r\n \r\n
\ \r\n and\r\n \r\n
\ \r\n $$\\alpha
<\\frac{3}{2}$$\r\n \r\n
\ \r\n α\r\n
\ <\r\n \r\n
\ 3\r\n 2\r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n , for all suitably
regular initial data of arbitrary size a statement on global existence of a global
weak solution is derived. By particularly covering the thermodynamically consistent
choice\r\n \r\n \r\n
\ $$f\\equiv id$$\r\n \r\n \r\n
\ f\r\n ≡\r\n
\ i\r\n d\r\n
\ \r\n \r\n
\ \r\n \r\n
\ of predominant physical relevance, this appears to go beyond
previous related literature which seems to either rely on independence of\r\n
\ \r\n \r\n
\ $$\\gamma $$\r\n \r\n γ\r\n
\ \r\n \r\n
\ \r\n on\r\n \r\n
\ \r\n $$\\Theta
$$\r\n \r\n
\ Θ\r\n \r\n
\ \r\n \r\n
\ , or to operate on finite time intervals.\r\n "
article_number: '192'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Large-data solutions in one-dimensional thermoviscoelasticity involving
temperature-dependent viscosities. Zeitschrift für angewandte Mathematik und
Physik. 2025;76(5). doi:10.1007/s00033-025-02582-y
apa: Winkler, M. (2025). Large-data solutions in one-dimensional thermoviscoelasticity
involving temperature-dependent viscosities. Zeitschrift Für Angewandte Mathematik
Und Physik, 76(5), Article 192. https://doi.org/10.1007/s00033-025-02582-y
bibtex: '@article{Winkler_2025, title={Large-data solutions in one-dimensional thermoviscoelasticity
involving temperature-dependent viscosities}, volume={76}, DOI={10.1007/s00033-025-02582-y},
number={5192}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }'
chicago: Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity
Involving Temperature-Dependent Viscosities.” Zeitschrift Für Angewandte Mathematik
Und Physik 76, no. 5 (2025). https://doi.org/10.1007/s00033-025-02582-y.
ieee: 'M. Winkler, “Large-data solutions in one-dimensional thermoviscoelasticity
involving temperature-dependent viscosities,” Zeitschrift für angewandte Mathematik
und Physik, vol. 76, no. 5, Art. no. 192, 2025, doi: 10.1007/s00033-025-02582-y.'
mla: Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity
Involving Temperature-Dependent Viscosities.” Zeitschrift Für Angewandte Mathematik
Und Physik, vol. 76, no. 5, 192, Springer Science and Business Media LLC,
2025, doi:10.1007/s00033-025-02582-y.
short: M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 76 (2025).
date_created: 2025-12-18T19:03:19Z
date_updated: 2026-04-23T12:20:44Z
doi: 10.1007/s00033-025-02582-y
intvolume: ' 76'
issue: '5'
language:
- iso: eng
project:
- _id: '245'
name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
für Leistungsschallanwendungen (NEPTUN)'
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: Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent
viscosities
type: journal_article
user_id: '31496'
volume: 76
year: '2025'
...
---
_id: '63283'
abstract:
- lang: eng
text: "AbstractThe parabolic problem $$\\begin{aligned}
\\left\\{ \\begin{array}{l} u_t=\\Delta \\big (u\\phi (v)\\big ), \\\\ v_t=\\Delta
v-uv, \\end{array} \\right. \\end{aligned}$$\r\n
\ \r\n \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ u\r\n t\r\n
\ \r\n =\r\n
\ Δ\r\n \r\n
\ (\r\n \r\n
\ u\r\n ϕ\r\n
\ \r\n (\r\n
\ v\r\n )\r\n
\ \r\n \r\n
\ )\r\n \r\n
\ ,\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n v\r\n
\ t\r\n \r\n
\ =\r\n Δ\r\n
\ v\r\n -\r\n
\ u\r\n v\r\n
\ ,\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n \r\n
\ is considered
in smoothly bounded subdomains of $${\\mathbb
{R}}^n$$\r\n
\ \r\n \r\n R\r\n
\ \r\n n\r\n
\ \r\n
with arbitrary $$n\\ge
1$$\r\n
\ \r\n n\r\n ≥\r\n
\ 1\r\n \r\n .
Under the assumptions that $$\\phi
\\in C^0([0,\\infty )) \\cap C^3((0,\\infty ))$$\r\n
\ \r\n ϕ\r\n ∈\r\n
\ \r\n C\r\n
\ 0\r\n \r\n
\ \r\n (\r\n
\ \r\n [\r\n
\ 0\r\n ,\r\n
\ ∞\r\n )\r\n
\ \r\n )\r\n
\ \r\n ∩\r\n
\ \r\n C\r\n
\ 3\r\n \r\n
\ \r\n (\r\n
\ \r\n (\r\n
\ 0\r\n ,\r\n
\ ∞\r\n )\r\n
\ \r\n )\r\n
\ \r\n \r\n
is positive on $$(0,\\infty
)$$\r\n
\ \r\n (\r\n 0\r\n
\ ,\r\n ∞\r\n
\ )\r\n \r\n
and satisfies $$\\begin{aligned}
\\liminf _{\\xi \\searrow 0} \\frac{\\phi (\\xi )}{\\xi ^\\alpha }>0 \\quad
{\\text{ and }} \\quad \\limsup _{\\xi \\searrow 0} \\big \\{ \\xi ^\\beta |\\phi
'(\\xi )| \\big \\}<\\infty \\end{aligned}$$\r\n
\ \r\n \r\n \r\n
\ \r\n \r\n
\ \r\n lim
inf\r\n \r\n ξ\r\n
\ ↘\r\n 0\r\n
\ \r\n \r\n
\ \r\n \r\n
\ ϕ\r\n (\r\n
\ ξ\r\n )\r\n
\ \r\n \r\n
\ ξ\r\n α\r\n
\ \r\n \r\n
\ >\r\n 0\r\n
\ \r\n \r\n
\ \r\n and\r\n
\ \r\n \r\n
\ \r\n \r\n
\ lim sup\r\n \r\n
\ ξ\r\n ↘\r\n
\ 0\r\n \r\n
\ \r\n \r\n
\ {\r\n \r\n
\ \r\n ξ\r\n
\ β\r\n \r\n
\ \r\n |\r\n
\ \r\n ϕ\r\n
\ ′\r\n \r\n
\ \r\n (\r\n
\ ξ\r\n )\r\n
\ \r\n |\r\n
\ \r\n \r\n
\ }\r\n \r\n
\ <\r\n ∞\r\n
\ \r\n \r\n
\ \r\n \r\n \r\n
\ with some $$\\alpha
>0$$\r\n
\ \r\n α\r\n >\r\n
\ 0\r\n \r\n
and $$\\beta >0$$\r\n \r\n
\ β\r\n >\r\n
\ 0\r\n \r\n ,
for all reasonably regular initial data an associated no-flux type initial-boundary
value problem is shown to admit a global solution in an appropriately generalized
sense. This extends previously developed solution theories on problems of this
form, which either concentrated on non-degenerate or weakly degenerate cases corresponding
to the choices $$\\alpha
=0$$\r\n
\ \r\n α\r\n =\r\n
\ 0\r\n \r\n
and $$\\alpha \\in (0,2)$$\r\n \r\n
\ α\r\n ∈\r\n
\ (\r\n 0\r\n
\ ,\r\n 2\r\n
\ )\r\n \r\n ,
or were restricted to low-dimensional settings by requiring that $$n\\le
2$$\r\n
\ \r\n n\r\n ≤\r\n
\ 2\r\n \r\n ."
article_number: '32'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Global generalized solvability in a strongly degenerate taxis-type
parabolic system modeling migration–consumption interaction. Zeitschrift für
angewandte Mathematik und Physik. 2023;74(1). doi:10.1007/s00033-022-01925-3
apa: Winkler, M. (2023). Global generalized solvability in a strongly degenerate
taxis-type parabolic system modeling migration–consumption interaction. Zeitschrift
Für Angewandte Mathematik Und Physik, 74(1), Article 32. https://doi.org/10.1007/s00033-022-01925-3
bibtex: '@article{Winkler_2023, title={Global generalized solvability in a strongly
degenerate taxis-type parabolic system modeling migration–consumption interaction},
volume={74}, DOI={10.1007/s00033-022-01925-3},
number={132}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
Science and Business Media LLC}, author={Winkler, Michael}, year={2023} }'
chicago: Winkler, Michael. “Global Generalized Solvability in a Strongly Degenerate
Taxis-Type Parabolic System Modeling Migration–Consumption Interaction.” Zeitschrift
Für Angewandte Mathematik Und Physik 74, no. 1 (2023). https://doi.org/10.1007/s00033-022-01925-3.
ieee: 'M. Winkler, “Global generalized solvability in a strongly degenerate taxis-type
parabolic system modeling migration–consumption interaction,” Zeitschrift für
angewandte Mathematik und Physik, vol. 74, no. 1, Art. no. 32, 2023, doi:
10.1007/s00033-022-01925-3.'
mla: Winkler, Michael. “Global Generalized Solvability in a Strongly Degenerate
Taxis-Type Parabolic System Modeling Migration–Consumption Interaction.” Zeitschrift
Für Angewandte Mathematik Und Physik, vol. 74, no. 1, 32, Springer Science
and Business Media LLC, 2023, doi:10.1007/s00033-022-01925-3.
short: M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 74 (2023).
date_created: 2025-12-18T19:17:51Z
date_updated: 2025-12-18T20:12:20Z
doi: 10.1007/s00033-022-01925-3
intvolume: ' 74'
issue: '1'
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: Global generalized solvability in a strongly degenerate taxis-type parabolic
system modeling migration–consumption interaction
type: journal_article
user_id: '31496'
volume: 74
year: '2023'
...
---
_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'
...
---
_id: '34675'
article_number: '135'
author:
- first_name: Tobias
full_name: Black, Tobias
id: '23686'
last_name: Black
orcid: 0000-0001-9963-0800
- first_name: Chunyan
full_name: Wu, Chunyan
last_name: Wu
citation:
ama: 'Black T, Wu C. Prescribed signal concentration on the boundary: Weak solvability
in a chemotaxis-Stokes system with proliferation. Zeitschrift für angewandte
Mathematik und Physik. 2021;72(4). doi:10.1007/s00033-021-01565-z'
apa: 'Black, T., & Wu, C. (2021). Prescribed signal concentration on the boundary:
Weak solvability in a chemotaxis-Stokes system with proliferation. Zeitschrift
Für Angewandte Mathematik Und Physik, 72(4), Article 135. https://doi.org/10.1007/s00033-021-01565-z'
bibtex: '@article{Black_Wu_2021, title={Prescribed signal concentration on the boundary:
Weak solvability in a chemotaxis-Stokes system with proliferation}, volume={72},
DOI={10.1007/s00033-021-01565-z},
number={4135}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
Science and Business Media LLC}, author={Black, Tobias and Wu, Chunyan}, year={2021}
}'
chicago: 'Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the
Boundary: Weak Solvability in a Chemotaxis-Stokes System with Proliferation.”
Zeitschrift Für Angewandte Mathematik Und Physik 72, no. 4 (2021). https://doi.org/10.1007/s00033-021-01565-z.'
ieee: 'T. Black and C. Wu, “Prescribed signal concentration on the boundary: Weak
solvability in a chemotaxis-Stokes system with proliferation,” Zeitschrift
für angewandte Mathematik und Physik, vol. 72, no. 4, Art. no. 135, 2021,
doi: 10.1007/s00033-021-01565-z.'
mla: 'Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary:
Weak Solvability in a Chemotaxis-Stokes System with Proliferation.” Zeitschrift
Für Angewandte Mathematik Und Physik, vol. 72, no. 4, 135, Springer Science
and Business Media LLC, 2021, doi:10.1007/s00033-021-01565-z.'
short: T. Black, C. Wu, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).
date_created: 2022-12-21T09:48:45Z
date_updated: 2023-07-10T11:39:30Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1007/s00033-021-01565-z
intvolume: ' 72'
issue: '4'
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: 'Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes
system with proliferation'
type: journal_article
user_id: '23686'
volume: 72
year: '2021'
...
---
_id: '63377'
article_number: '40'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Finite-time blow-up in low-dimensional Keller–Segel systems with
logistic-type superlinear degradation. Zeitschrift für angewandte Mathematik
und Physik. 2018;69(2). doi:10.1007/s00033-018-0935-8
apa: Winkler, M. (2018). Finite-time blow-up in low-dimensional Keller–Segel systems
with logistic-type superlinear degradation. Zeitschrift Für Angewandte Mathematik
Und Physik, 69(2), Article 40. https://doi.org/10.1007/s00033-018-0935-8
bibtex: '@article{Winkler_2018, title={Finite-time blow-up in low-dimensional Keller–Segel
systems with logistic-type superlinear degradation}, volume={69}, DOI={10.1007/s00033-018-0935-8},
number={240}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
Science and Business Media LLC}, author={Winkler, Michael}, year={2018} }'
chicago: Winkler, Michael. “Finite-Time Blow-up in Low-Dimensional Keller–Segel
Systems with Logistic-Type Superlinear Degradation.” Zeitschrift Für Angewandte
Mathematik Und Physik 69, no. 2 (2018). https://doi.org/10.1007/s00033-018-0935-8.
ieee: 'M. Winkler, “Finite-time blow-up in low-dimensional Keller–Segel systems
with logistic-type superlinear degradation,” Zeitschrift für angewandte Mathematik
und Physik, vol. 69, no. 2, Art. no. 40, 2018, doi: 10.1007/s00033-018-0935-8.'
mla: Winkler, Michael. “Finite-Time Blow-up in Low-Dimensional Keller–Segel Systems
with Logistic-Type Superlinear Degradation.” Zeitschrift Für Angewandte Mathematik
Und Physik, vol. 69, no. 2, 40, Springer Science and Business Media LLC, 2018,
doi:10.1007/s00033-018-0935-8.
short: M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 69 (2018).
date_created: 2025-12-19T11:06:58Z
date_updated: 2025-12-19T11:07:05Z
doi: 10.1007/s00033-018-0935-8
intvolume: ' 69'
issue: '2'
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: Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type
superlinear degradation
type: journal_article
user_id: '31496'
volume: 69
year: '2018'
...