Generalised global supersolutions with mass control for systems with taxis

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.

arXiv admin note: text overlap with arXiv:1804.05333 Changes: $v>0$ a.e. in Definition 3.1 and corrections in the convergence arguments in Section 5.2

References in corpus (2)

• Global existence for a degenerate haptotaxis model of cancer invasion
• Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity

Cited by in corpus (3)

• Global solvability in a two-species chemotaxis system with signal production
• Mathematical models for cell migration: a nonlocal perspective
• Immediate smoothing and global solutions for initial data in $L^1\times W^{1,2}$ in a Keller-Segel system with logistic terms in 2D