Global Existence of Solutions to a One-Species and Two-Chemicals Chemotaxis System with Singular Sensitivity and Logistic Source

The research paper investigates the global existence of solutions to a parabolic-elliptic-elliptic chemotaxis system that describes the interaction of a single species with two chemical substances in a smoothly bounded domain. The system under consideration incorporates singular sensitivity functions, which pose significant analytical challenges.In this study, the global existence of positive classical solutions under specific parameter constraints is established. The paper employs rigorous mathematical analysis to derive sufficient conditions that ensure the well-posedness of the associated initial value problem (IVP).The results contribute to the theoretical understanding of chemotaxis models with singular sensitivities, which are relevant in biological and ecological contexts.