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- W4300111166 abstract "The chemotaxis system [ left{ begin{array}{l} u_t = Delta u - chinabla cdot (frac{u}{v}nabla v), v_t=Delta v - v+u, end{array} right. ] is considered in a bounded domain $Omegasubset mathbb{R}^n$ with smooth boundary, where $chi>0$. An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter $chi$ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that[ chi < left{ begin{array}{ll} infty qquad & mbox{if } n=2, sqrt{8} qquad & mbox{if } n=3, frac{n}{n-2} qquad & mbox{if } nge 4, end{array} right. ] for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized solution. This solution inter alia has the property that [ uin L^1_{loc}(barOmegatimes [0,infty)). ]" @default.
- W4300111166 created "2022-10-03" @default.
- W4300111166 creator A5041353240 @default.
- W4300111166 creator A5071892237 @default.
- W4300111166 date "2017-01-25" @default.
- W4300111166 modified "2023-10-16" @default.
- W4300111166 title "A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: Global solvability for large nonradial data" @default.
- W4300111166 doi "https://doi.org/10.48550/arxiv.1701.07391" @default.
- W4300111166 hasPublicationYear "2017" @default.
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