English

Generalised global supersolutions with mass control for systems with taxis

Analysis of PDEs 2023-02-23 v5

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.

Keywords

Cite

@article{arxiv.1806.06715,
  title  = {Generalised global supersolutions with mass control for systems with taxis},
  author = {Anna Zhigun},
  journal= {arXiv preprint arXiv:1806.06715},
  year   = {2023}
}

Comments

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