Generalised global supersolutions with mass control for systems with taxis

TL;DR

This paper establishes the existence of generalized global supersolutions with mass control for a broad class of chemotaxis systems, including Keller-Segel models, enabling analysis beyond blow-up times.

Contribution

It introduces a novel construction of supersolutions with mass control that extends the solvability of chemotaxis systems beyond classical blow-up scenarios.

Findings

Supersolutions coincide with classical solutions when smooth.

Construction applies to Keller-Segel and chemorepellent models.

Provides a framework for global existence beyond blow-up.

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.