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The existence of generalised global supersolutions with a control upon thetotal muss is established for the parabolic-parabolic Keller-Segel system withlogarithmic sensitivity for any space dimension. It is verified that smoothsupersolutions of this sort are actually classical solutions. Unlike thepreviously existing constructions, neither is the chemotactic sensitivitycoefficient required to be small, nor is it necessary for the initial data tobe radially symmetric.  Keywords: chemotaxis; generalised supersolution; global existence;logarithmic sensitivity

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