{"page":"33-57","language":[{"iso":"eng"}],"publication":"Asymptotic Analysis","status":"public","_id":"53335","user_id":"31496","year":"2022","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>","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={IOS Press}, author={Winkler, Michael}, year={2022}, pages={33–57} }","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>.","short":"M. Winkler, Asymptotic Analysis 131 (2022) 33–57.","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, IOS Press, 2022, pp. 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>."},"type":"journal_article","keyword":["General Mathematics"],"publisher":"IOS Press","issue":"1","intvolume":"       131","date_updated":"2024-04-07T12:47:01Z","title":"Exponential grow-up rates in a quasilinear Keller–Segel system","abstract":[{"lang":"eng","text":"<jats:p>The chemotaxis system ( ⋆ ) u t = ∇ · ( D ( u ) ∇ u ) − ∇ · ( u S ( u ) ∇ v ) , 0 = Δ v − μ + u , μ = 1 | Ω | ∫ Ω u , is considered in a ball Ω = B R ( 0 ) ⊂ R n . It is shown that if S ∈ C 2 ( [ 0 , ∞ ) ) suitably generalizes the prototype given by S ( ξ ) = χ ξ + 1 , ξ ⩾ 0 , with some χ &gt; 0, and if diffusion is suitably weak in the sense that 0 &lt; D ∈ C 2 ( ( 0 , ∞ ) ) is such that there exist K D &gt; 0 and m ∈ ( − ∞ , 1 − 2 n ) fulfilling D ( ξ ) ⩽ K D ξ m − 1 for all  ξ &gt; 0 , then for appropriate choices of sufficiently concentrated initial data, an associated no-flux initial-boundary value problem admits a global classical solution ( u , v ) which blows up in infinite time and satisfies 1 C e χ t ⩽ ‖ u ( · , t ) ‖ L ∞ ( Ω ) ⩽ C e χ t for all  t &gt; 0 . 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>"}],"publication_status":"published","doi":"10.3233/asy-221765","date_created":"2024-04-07T12:46:57Z","publication_identifier":{"issn":["1875-8576","0921-7134"]},"author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"volume":131}