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Mathematics > Analysis of PDEs

arXiv:1804.05333 (math)
[Submitted on 15 Apr 2018]

Title:Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity

Authors:Anna Zhigun
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Abstract:The existence of generalised global supersolutions with a control upon the total muss is established for the parabolic-parabolic Keller-Segel system with logarithmic sensitivity for any space dimension. It is verified that smooth supersolutions of this sort are actually classical solutions. Unlike the previously existing constructions, neither is the chemotactic sensitivity coefficient required to be small, nor is it necessary for the initial data to be radially symmetric.
Keywords: chemotaxis; generalised supersolution; global existence; logarithmic sensitivity
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35B45, 92C17, 35D30, 35D99, 35K55
Cite as: arXiv:1804.05333 [math.AP]
  (or arXiv:1804.05333v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.05333
Related DOI: https://doi.org/10.1016/j.jmaa.2018.08.001

Submission history

From: Anna Zhigun [view email]
[v1] Sun, 15 Apr 2018 10:24:45 UTC (19 KB)
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