[{"type":"journal_article","publication":"Asymptotic Analysis","status":"public","abstract":[{"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>","lang":"eng"}],"user_id":"31496","_id":"63286","language":[{"iso":"eng"}],"issue":"1","publication_status":"published","publication_identifier":{"issn":["0921-7134","1875-8576"]},"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>","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>.","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>","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.","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} }"},"page":"33-57","intvolume":"       131","year":"2022","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"date_created":"2025-12-18T19:18:51Z","volume":131,"publisher":"SAGE Publications","date_updated":"2025-12-18T20:07:19Z","doi":"10.3233/asy-221765","title":"Exponential grow-up rates in a quasilinear Keller–Segel system"}]