Abstract: The Riemann problem of a simplified chemotaxis model with Dirac initial value was discussed  by using phase-plane analysis method and generalized Rankine-Hugoniot conditions. According to the relationship between the initial values q_±,q₀ and 0, we divided the Riemann problem into five cases and obtained the global solutions of the problem constructively. Finally,  numerical simulations were used to verify the correctness of the theoretical results.

Key words: phase-plane analysis, Rankine-Hugoniot condition, Dirac initial value, chemotaxis model, numerical simulation