---
_id: '63286'
abstract:
- lang: eng
  text: '<jats:p> The chemotaxis system [Formula: see text] is considered in a ball
    [Formula: see text]. </jats:p><jats:p> It is shown that if [Formula: see text]
    suitably generalizes the prototype given by [Formula: see text] with some [Formula:
    see text], and if diffusion is suitably weak in the sense that [Formula: see text]
    is such that there exist [Formula: see text] and [Formula: see text] fulfilling
    [Formula: see text] then for appropriate choices of sufficiently concentrated
    initial data, an associated no-flux initial-boundary value problem admits a global
    classical solution [Formula: see text] which blows up in infinite time and satisfies
    [Formula: see text] A major part of the proof is based on a comparison argument
    involving explicitly constructed subsolutions to a scalar parabolic problem satisfied
    by mass accumulation functions corresponding to solutions of ( ⋆ ). </jats:p>'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Exponential grow-up rates in a quasilinear Keller–Segel system.
    <i>Asymptotic Analysis</i>. 2022;131(1):33-57. doi:<a href="https://doi.org/10.3233/asy-221765">10.3233/asy-221765</a>
  apa: Winkler, M. (2022). Exponential grow-up rates in a quasilinear Keller–Segel
    system. <i>Asymptotic Analysis</i>, <i>131</i>(1), 33–57. <a href="https://doi.org/10.3233/asy-221765">https://doi.org/10.3233/asy-221765</a>
  bibtex: '@article{Winkler_2022, title={Exponential grow-up rates in a quasilinear
    Keller–Segel system}, volume={131}, DOI={<a href="https://doi.org/10.3233/asy-221765">10.3233/asy-221765</a>},
    number={1}, journal={Asymptotic Analysis}, publisher={SAGE Publications}, author={Winkler,
    Michael}, year={2022}, pages={33–57} }'
  chicago: 'Winkler, Michael. “Exponential Grow-up Rates in a Quasilinear Keller–Segel
    System.” <i>Asymptotic Analysis</i> 131, no. 1 (2022): 33–57. <a href="https://doi.org/10.3233/asy-221765">https://doi.org/10.3233/asy-221765</a>.'
  ieee: 'M. Winkler, “Exponential grow-up rates in a quasilinear Keller–Segel system,”
    <i>Asymptotic Analysis</i>, vol. 131, no. 1, pp. 33–57, 2022, doi: <a href="https://doi.org/10.3233/asy-221765">10.3233/asy-221765</a>.'
  mla: Winkler, Michael. “Exponential Grow-up Rates in a Quasilinear Keller–Segel
    System.” <i>Asymptotic Analysis</i>, vol. 131, no. 1, SAGE Publications, 2022,
    pp. 33–57, doi:<a href="https://doi.org/10.3233/asy-221765">10.3233/asy-221765</a>.
  short: M. Winkler, Asymptotic Analysis 131 (2022) 33–57.
date_created: 2025-12-18T19:18:51Z
date_updated: 2025-12-18T20:07:19Z
doi: 10.3233/asy-221765
intvolume: '       131'
issue: '1'
language:
- iso: eng
page: 33-57
publication: Asymptotic Analysis
publication_identifier:
  issn:
  - 0921-7134
  - 1875-8576
publication_status: published
publisher: SAGE Publications
status: public
title: Exponential grow-up rates in a quasilinear Keller–Segel system
type: journal_article
user_id: '31496'
volume: 131
year: '2022'
...