Boundedness and asymptotic stability of solutions in an alopecia areata chemotaxis system with signal-dependent sensitivity (Q6638330)

This work examines a three-component chemotaxis system modeling spatio-temporal Alopecia Areata dynamics with signal-dependent sensitivity under homogeneous Neumann boundary conditions in a smoothly bounded domain \( \Omega \subset \mathbb{R}^n \) (\( n \geq 1 \)). For smooth chemotactic functions \( \chi_i(w) \) (\( i = 1, 2 \)) satisfying specific conditions and suitable initial data, the system is shown to admit a unique global bounded classical solution. Additionally, using an appropriate energy function, it is proven that the unique coexistence equilibrium is globally convergent within a certain parameter regime, extending and improving existing results in the literature.