TY - JOUR

T1 - A generalized solution concept for the Keller–Segel system with logarithmic sensitivity

T2 - global solvability for large nonradial data

AU - Lankeit, Johannes

AU - Winkler, Michael

PY - 2017/7/20

Y1 - 2017/7/20

N2 - The chemotaxis system (Formula presented.) is considered in a bounded domain Ω ⊂ Rn with smooth boundary, where χ> 0. An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter χ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that (Formula presented.) 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 (Formula presented.).

AB - The chemotaxis system (Formula presented.) is considered in a bounded domain Ω ⊂ Rn with smooth boundary, where χ> 0. An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter χ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that (Formula presented.) 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 (Formula presented.).

KW - Chemotaxis

KW - Generalized solution

KW - Global existence

KW - Logarithmic sensitivity

UR - http://www.scopus.com/inward/record.url?scp=85025106709&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1701.07391

DO - 10.48550/arXiv.1701.07391

M3 - Article

AN - SCOPUS:85025106709

VL - 24

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

SN - 1021-9722

M1 - 49

ER -