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arXiv · 1806.06715

Generalised global supersolutions with mass control for systems with taxis

Anna Zhigun
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Abstract

The existence of generalised global supersolutions with a control upon the total mass is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that as long as a supersolution of this sort remains smooth, it coincides with the classical solution. At the same time, the proposed construction provides solvability beyond a blow-up time. The considered class of systems includes the basic form of the Keller-Segel model as well as the case of a chemorepellent.

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Anna Zhigun. 2018-06-15. Generalised global supersolutions with mass control for systems with taxis. https://doi.org/10.1137/18m1217826

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