ON THE EXISTENCE OF WEAK SOLUTIONS FOR THE KINETIC MODELS OF THE MOTION OF MYXOBACTERIA WITH ALIGNMENT AND REVERSALS
Publication Date
1-1-2025
Document Type
Article
Publication Title
Kinetic and Related Models
Volume
18
Issue
5
DOI
10.3934/krm.2025001
First Page
692
Last Page
705
Abstract
In this paper, we consider two non-linear kinetic partial differential equations that emerge in modeling rod-shaped bacteria’s motion. Their motion is characterized by nematic alignment with neighboring bacteria, orientation reversals from cell polarity switching, and orientation diffusion. Our contribution lies in establishing the global existence of weak solutions for these equations. Our approach is based on applying the classical averaging lemma from the kinetic theory, augmented by a new version of that lemma, in which the transport operator is substituted with a uni-directional diffusion operator.
Funding Number
1903270
Funding Sponsor
National Science Foundation
Keywords
averaging lemmas, kinetic theory, mean-field equations, Models for bacterial motion, multi-agent interacting systems
Department
Mathematics and Statistics
Recommended Citation
Misha Perepelitsa, Ilya Timofeyev, Patrick Murphy, and Oleg A. Igoshin. "ON THE EXISTENCE OF WEAK SOLUTIONS FOR THE KINETIC MODELS OF THE MOTION OF MYXOBACTERIA WITH ALIGNMENT AND REVERSALS" Kinetic and Related Models (2025): 692-705. https://doi.org/10.3934/krm.2025001
