---
_id: '63312'
abstract:
- lang: eng
text: "<p style='text-indent:20px;'>The chemotaxis
system</p><p style='text-indent:20px;'><disp-formula> <label/>
<tex-math id=\"FE1\"> \\begin{document}$ \\begin{array}{l}\\left\\{ \\begin{array}{l}
\tu_t = \\nabla \\cdot \\big( D(u) \\nabla u \\big) - \\nabla \\cdot \\big( uS(x,
u, v)\\cdot \\nabla v\\big), \\\\ \tv_t = \\Delta v -uv, \\end{array} \\right.
\\end{array} $\\end{document} </tex-math></disp-formula></p><p
style='text-indent:20px;'>is considered in a bounded domain <inline-formula><tex-math
id=\"M1\">\\begin{document}$ \\Omega\\subset \\mathbb{R}^n $\\end{document}</tex-math></inline-formula>,
<inline-formula><tex-math id=\"M2\">\\begin{document}$ n\\ge 2 $\\end{document}</tex-math></inline-formula>,
with smooth boundary.</p><p style='text-indent:20px;'>It is shown
that if <inline-formula><tex-math id=\"M3\">\\begin{document}$ D:
[0, \\infty) \\to [0, \\infty) $\\end{document}</tex-math></inline-formula>
and <inline-formula><tex-math id=\"M4\">\\begin{document}$ S: \\overline{\\Omega}\\times
[0, \\infty)\\times (0, \\infty)\\to \\mathbb{R}^{n\\times n} $\\end{document}</tex-math></inline-formula>
are suitably smooth functions satisfying</p><p style='text-indent:20px;'><disp-formula>
<label/> <tex-math id=\"FE2\"> \\begin{document}$ \\begin{array}{l}D(u)
\\ge k_D u^{m-1} \t\\qquad {\\rm{for\\; all}}\\; u\\ge 0 \\end{array} $\\end{document}
</tex-math></disp-formula></p><p style='text-indent:20px;'>and</p><p
style='text-indent:20px;'><disp-formula> <label/> <tex-math
id=\"FE3\"> \\begin{document}$ \\begin{array}{l}|S(x, u, v)| \\le \\frac{S_0(v)}{v^\\alpha}
\\qquad {\\rm{for\\; all}}\\; (x, u, v)\\; \\in \\Omega\\times (0, \\infty)^2
\\end{array} $\\end{document} </tex-math></disp-formula></p><p
style='text-indent:20px;'>with some</p><p style='text-indent:20px;'><disp-formula>
<label/> <tex-math id=\"FE4\"> \\begin{document}$ \\begin{array}{l}m>\\frac{3n-2}{2n}
\t\\qquad {\\rm{and}}\\;\\alpha\\in [0, 1), \\end{array} $\\end{document} </tex-math></disp-formula></p><p
style='text-indent:20px;'>and with some <inline-formula><tex-math
id=\"M5\">\\begin{document}$ k_D>0 $\\end{document}</tex-math></inline-formula>
and nondecreasing <inline-formula><tex-math id=\"M6\">\\begin{document}$
S_0: (0, \\infty)\\to (0, \\infty) $\\end{document}</tex-math></inline-formula>,
then for all suitably regular initial data a corresponding no-flux type initial-boundary
value problem admits a global bounded weak solution which actually is smooth and
classical if <inline-formula><tex-math id=\"M7\">\\begin{document}$
D(0)>0 $\\end{document}</tex-math></inline-formula>.</p>"
article_number: '6565'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. Approaching logarithmic singularities in quasilinear chemotaxis-consumption
systems with signal-dependent sensitivities. Discrete and Continuous Dynamical
Systems - B. 2022;27(11). doi:10.3934/dcdsb.2022009
apa: Winkler, M. (2022). Approaching logarithmic singularities in quasilinear chemotaxis-consumption
systems with signal-dependent sensitivities. Discrete and Continuous Dynamical
Systems - B, 27(11), Article 6565. https://doi.org/10.3934/dcdsb.2022009
bibtex: '@article{Winkler_2022, title={Approaching logarithmic singularities in
quasilinear chemotaxis-consumption systems with signal-dependent sensitivities},
volume={27}, DOI={10.3934/dcdsb.2022009},
number={116565}, journal={Discrete and Continuous Dynamical Systems - B}, publisher={American
Institute of Mathematical Sciences (AIMS)}, author={Winkler, Michael}, year={2022}
}'
chicago: Winkler, Michael. “Approaching Logarithmic Singularities in Quasilinear
Chemotaxis-Consumption Systems with Signal-Dependent Sensitivities.” Discrete
and Continuous Dynamical Systems - B 27, no. 11 (2022). https://doi.org/10.3934/dcdsb.2022009.
ieee: 'M. Winkler, “Approaching logarithmic singularities in quasilinear chemotaxis-consumption
systems with signal-dependent sensitivities,” Discrete and Continuous Dynamical
Systems - B, vol. 27, no. 11, Art. no. 6565, 2022, doi: 10.3934/dcdsb.2022009.'
mla: Winkler, Michael. “Approaching Logarithmic Singularities in Quasilinear Chemotaxis-Consumption
Systems with Signal-Dependent Sensitivities.” Discrete and Continuous Dynamical
Systems - B, vol. 27, no. 11, 6565, American Institute of Mathematical Sciences
(AIMS), 2022, doi:10.3934/dcdsb.2022009.
short: M. Winkler, Discrete and Continuous Dynamical Systems - B 27 (2022).
date_created: 2025-12-18T19:30:32Z
date_updated: 2025-12-18T20:05:47Z
doi: 10.3934/dcdsb.2022009
intvolume: ' 27'
issue: '11'
language:
- iso: eng
publication: Discrete and Continuous Dynamical Systems - B
publication_identifier:
issn:
- 1531-3492
- 1553-524X
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Approaching logarithmic singularities in quasilinear chemotaxis-consumption
systems with signal-dependent sensitivities
type: journal_article
user_id: '31496'
volume: 27
year: '2022'
...
---
_id: '63330'
author:
- first_name: Genglin
full_name: Li, Genglin
last_name: Li
- first_name: Youshan
full_name: Tao, Youshan
last_name: Tao
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Li G, Tao Y, Winkler M. Large time behavior in a predator-prey system with
indirect pursuit-evasion interaction. Discrete and Continuous Dynamical Systems
- B. 2020;25(11):4383-4396. doi:10.3934/dcdsb.2020102
apa: Li, G., Tao, Y., & Winkler, M. (2020). Large time behavior in a predator-prey
system with indirect pursuit-evasion interaction. Discrete and Continuous Dynamical
Systems - B, 25(11), 4383–4396. https://doi.org/10.3934/dcdsb.2020102
bibtex: '@article{Li_Tao_Winkler_2020, title={Large time behavior in a predator-prey
system with indirect pursuit-evasion interaction}, volume={25}, DOI={10.3934/dcdsb.2020102},
number={11}, journal={Discrete and Continuous Dynamical Systems - B}, publisher={American
Institute of Mathematical Sciences (AIMS)}, author={Li, Genglin and Tao, Youshan
and Winkler, Michael}, year={2020}, pages={4383–4396} }'
chicago: 'Li, Genglin, Youshan Tao, and Michael Winkler. “Large Time Behavior in
a Predator-Prey System with Indirect Pursuit-Evasion Interaction.” Discrete
and Continuous Dynamical Systems - B 25, no. 11 (2020): 4383–96. https://doi.org/10.3934/dcdsb.2020102.'
ieee: 'G. Li, Y. Tao, and M. Winkler, “Large time behavior in a predator-prey system
with indirect pursuit-evasion interaction,” Discrete and Continuous Dynamical
Systems - B, vol. 25, no. 11, pp. 4383–4396, 2020, doi: 10.3934/dcdsb.2020102.'
mla: Li, Genglin, et al. “Large Time Behavior in a Predator-Prey System with Indirect
Pursuit-Evasion Interaction.” Discrete and Continuous Dynamical Systems - B,
vol. 25, no. 11, American Institute of Mathematical Sciences (AIMS), 2020, pp.
4383–96, doi:10.3934/dcdsb.2020102.
short: G. Li, Y. Tao, M. Winkler, Discrete and Continuous Dynamical Systems - B
25 (2020) 4383–4396.
date_created: 2025-12-18T19:38:22Z
date_updated: 2025-12-18T20:00:40Z
doi: 10.3934/dcdsb.2020102
intvolume: ' 25'
issue: '11'
language:
- iso: eng
page: 4383-4396
publication: Discrete and Continuous Dynamical Systems - B
publication_identifier:
issn:
- 1531-3492
- 1553-524X
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: Large time behavior in a predator-prey system with indirect pursuit-evasion
interaction
type: journal_article
user_id: '31496'
volume: 25
year: '2020'
...
---
_id: '17027'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Bianca
full_name: Thiere, Bianca
last_name: Thiere
citation:
ama: Dellnitz M, Junge O, Thiere B. The numerical detection of connecting orbits.
Discrete & Continuous Dynamical Systems - B. 2001;1(1531-3492_2001_1_125):125-135.
doi:10.3934/dcdsb.2001.1.125
apa: Dellnitz, M., Junge, O., & Thiere, B. (2001). The numerical detection of
connecting orbits. Discrete & Continuous Dynamical Systems - B, 1(1531-3492_2001_1_125),
125–135. https://doi.org/10.3934/dcdsb.2001.1.125
bibtex: '@article{Dellnitz_Junge_Thiere_2001, title={The numerical detection of
connecting orbits}, volume={1}, DOI={10.3934/dcdsb.2001.1.125},
number={1531-3492_2001_1_125}, journal={Discrete & Continuous Dynamical Systems
- B}, author={Dellnitz, Michael and Junge, Oliver and Thiere, Bianca}, year={2001},
pages={125–135} }'
chicago: 'Dellnitz, Michael, Oliver Junge, and Bianca Thiere. “The Numerical Detection
of Connecting Orbits.” Discrete & Continuous Dynamical Systems - B
1, no. 1531-3492_2001_1_125 (2001): 125–35. https://doi.org/10.3934/dcdsb.2001.1.125.'
ieee: M. Dellnitz, O. Junge, and B. Thiere, “The numerical detection of connecting
orbits,” Discrete & Continuous Dynamical Systems - B, vol. 1, no. 1531-3492_2001_1_125,
pp. 125–135, 2001.
mla: Dellnitz, Michael, et al. “The Numerical Detection of Connecting Orbits.” Discrete
& Continuous Dynamical Systems - B, vol. 1, no. 1531-3492_2001_1_125,
2001, pp. 125–35, doi:10.3934/dcdsb.2001.1.125.
short: M. Dellnitz, O. Junge, B. Thiere, Discrete & Continuous Dynamical Systems
- B 1 (2001) 125–135.
date_created: 2020-05-19T20:38:40Z
date_updated: 2022-01-06T06:53:02Z
doi: 10.3934/dcdsb.2001.1.125
intvolume: ' 1'
issue: 1531-3492_2001_1_125
language:
- iso: eng
page: 125-135
publication: Discrete & Continuous Dynamical Systems - B
publication_identifier:
issn:
- 1531-3492
publication_status: published
status: public
title: The numerical detection of connecting orbits
type: journal_article
user_id: '32829'
volume: 1
year: '2001'
...