Global Boundedness of a Two-species Parabolic Keller-Segel System with Gradient-dependent Singular Sensitivity and Indirect Signal Production

In this work, we investigate a two-species chemotaxis system with singular sensitivity and indirect signal production in an n-dimensional domain (n≥ 1) . The movement of each species is governed by a nonlinear sensitivity function that responds to chemical gradients. The chemical substances interact dynamically: one chemical is secreted by the species, while the other degrades over time and influences the movement. The model also incorporates logistic growth and interspecific competition between the species. Using semigroup theory and a Moser-type iteration framework, we establish the global boundedness of classical solutions.