Absence of blow-up in a fully parabolic chemotaxis system with weak singular sensitivity and logistic damping in dimension two

Absence of blow-up in a fully parabolic chemotaxis system with weak singular sensitivity and logistic damping in dimension two | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL Mathematical Methods in the Applied Sciences This is a preprint and has not been peer reviewed. Data may be preliminary. 17 June 2025 V1 Latest version Share on Absence of blow-up in a fully parabolic chemotaxis system with weak singular sensitivity and logistic damping in dimension two Author : Minh Le 0000-0003-4059-6294 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175018685.59588967/v1 187 views 256 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract It is shown in this paper that blow-up does not occur in the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain Ω ⊂ R 2 : { u t = ∆ u − χ ∇ · ( u v k ∇ v ) + ru − µ u 2, in Ω × ( 0, T max ), v t = ∆ v − αv + βu, in Ω × ( 0, T max ), where k ∈(0 , 1), and χ,r,µ,α,β are positive parameters. Known results have already established the same conclusion for the parabolic-elliptic case. Here, we complement these findings by extending the result to the fully parabolic case. Supplementary Material File (manuscript.pdf) Download 352.88 KB Information & Authors Information Version history V1 Version 1 17 June 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Collection Mathematical Methods in the Applied Sciences Keywords chemotaxis global boundedness global existence logistic sources weak singular sensitivity Authors Affiliations Minh Le 0000-0003-4059-6294 [email protected] Westlake University View all articles by this author Metrics & Citations Metrics Article Usage 187 views 256 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Minh Le. Absence of blow-up in a fully parabolic chemotaxis system with weak singular sensitivity and logistic damping in dimension two. Authorea . 17 June 2025. 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