Global solvability of a model for tuberculosis granuloma formation

authored by
Mario Fuest, Johannes Lankeit, Masaaki Mizukami
Abstract

We discuss a nonlinear system of partial differential equations modelling the formation of granuloma during tuberculosis infections and prove the global solvability of the homogeneous Neumann problem for ut=DuΔu−χu∇⋅(u∇v)−γuuv−δuu+βu,vt=DvΔv+ρvv−γvuv+μvw,wt=DwΔw+γwuv−αwwz−μww,zt=DzΔz−χz∇⋅(z∇w)+αzf(w)z−δzzin bounded domains in the classical and weak sense in the two- and three-dimensional setting, respectively. In order to derive suitable a priori estimates, we study the evolution of the well-known energy functional for the chemotaxis–consumption system both for the (u,v)- and the (z,w)-subsystem. A key challenge compared to “pure” consumption systems consists of overcoming the difficulties raised by the additional, in part positive, terms in the second and third equations. This is inter alia achieved by utilizing a dissipative term of the (quasi-)energy functional, which may just be discarded in simpler consumption systems.

Organisation(s)
Faculty of Mathematics and Physics
External Organisation(s)
Kyoto University of Education
Type
Article
Journal
Nonlinear Analysis: Real World Applications
Volume
85
ISSN
1468-1218
Publication date
28.03.2025
Publication status
E-pub ahead of print
Peer reviewed
Yes
ASJC Scopus subject areas
Analysis, General Engineering, General Economics,Econometrics and Finance, Computational Mathematics, Applied Mathematics
Sustainable Development Goals
SDG 3 - Good Health and Well-being
Electronic version(s)
https://doi.org/10.1016/j.nonrwa.2025.104369 (Access: Closed)
https://doi.org/ arXiv:2411.00542 (Access: Open)