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

TL;DR

This paper proves the existence of global supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity, without restrictions on sensitivity size or initial data symmetry, advancing understanding of chemotaxis models.

Contribution

It introduces a new framework for supersolutions with mass control applicable to any space dimension, removing previous limitations on sensitivity and initial data symmetry.

Findings

Existence of generalised global supersolutions with mass control

Supersolutions are classical solutions if smooth

No restriction on chemotactic sensitivity coefficient

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