Mathematical modeling of chemotaxis (the movement of biological cells in response to chemical gradients) has evolved into a modern discipline, aspects of which include its mechanistic basis, modeling of specific systems, and the mathematical behavior of the underlying equations. In this paper, we consider in detail the periodic variant of the Keller-Segel model. The global existence and uniqueness of the classical solutions of this system are proved by the contraction mapping principle together with Lₚ estimates and Schauder estimates of parabolic equations.
Takhirov et al. (2025) studied this question.