Stability and instability in a three-component chemotaxis model for alopecia areata

This paper investigates the stability and instability of a generalized reaction-diffusion-advection system that describes the spatio-temporal dynamics of alopecia areata lesions. Using the spectral analysis, we investigate the effect of chemotactic strengths on the stability and instability of a linearized problem around the positive constant equilibrium. We then extend our analysis to the nonlinear system, utilizing higher-order energy estimates and bootstrap techniques to study its stability and instability based on the linearized results. Additionally, we provide numerical simulations to support our theoretical results.