{"citation":{"mla":"Winkler, Michael. “Exponential Grow-up Rates in a Quasilinear Keller–Segel System.” Asymptotic Analysis, vol. 131, no. 1, IOS Press, 2022, pp. 33–57, doi:10.3233/asy-221765.","apa":"Winkler, M. (2022). Exponential grow-up rates in a quasilinear Keller–Segel system. Asymptotic Analysis, 131(1), 33–57. https://doi.org/10.3233/asy-221765","chicago":"Winkler, Michael. “Exponential Grow-up Rates in a Quasilinear Keller–Segel System.” Asymptotic Analysis 131, no. 1 (2022): 33–57. https://doi.org/10.3233/asy-221765.","ama":"Winkler M. Exponential grow-up rates in a quasilinear Keller–Segel system. Asymptotic Analysis. 2022;131(1):33-57. doi:10.3233/asy-221765","bibtex":"@article{Winkler_2022, title={Exponential grow-up rates in a quasilinear Keller–Segel system}, volume={131}, DOI={10.3233/asy-221765}, number={1}, journal={Asymptotic Analysis}, publisher={IOS Press}, author={Winkler, Michael}, year={2022}, pages={33–57} }","short":"M. Winkler, Asymptotic Analysis 131 (2022) 33–57.","ieee":"M. Winkler, “Exponential grow-up rates in a quasilinear Keller–Segel system,” Asymptotic Analysis, vol. 131, no. 1, pp. 33–57, 2022, doi: 10.3233/asy-221765."},"intvolume":" 131","publisher":"IOS Press","date_created":"2024-04-07T12:46:57Z","issue":"1","year":"2022","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"title":"Exponential grow-up rates in a quasilinear Keller–Segel system","publication":"Asymptotic Analysis","doi":"10.3233/asy-221765","date_updated":"2024-04-07T12:47:01Z","_id":"53335","abstract":[{"lang":"eng","text":"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 > 0, and if diffusion is suitably weak in the sense that 0 < D ∈ C 2 ( ( 0 , ∞ ) ) is such that there exist K D > 0 and m ∈ ( − ∞ , 1 − 2 n ) fulfilling D ( ξ ) ⩽ K D ξ m − 1 for all  ξ > 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 > 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 (⋆)."}],"publication_identifier":{"issn":["1875-8576","0921-7134"]},"volume":131,"language":[{"iso":"eng"}],"page":"33-57","publication_status":"published","type":"journal_article","user_id":"31496","keyword":["General Mathematics"],"status":"public"}