Blow-up and Lower Bounds of Solutions to a Two-Species Keller-Segel Chemotaxis Model in R^2 - Sathishkumar, G.; Shangerganesh, L.; Karthikeyan, S.; Nieto, J.J. (Journal of Applied Nonlinear Dynamics, 2026)
This paper investigates the blow-up phenomena of non-negative solutions of a two-species Keller-Segel chemotaxis model with the Lotka-Volterra competitive source terms under Neumann boundary conditions in a bounded domain ΩR^2 with smooth boundary. We establish the results for the finite time blow-up of solutions when χ_1α=χ_2β for some positive constants α and β. The concavity method determines the main result in a two-dimensional space domain with a suitable auxiliary function. Also, the lower bounds for the finite time blow-up of solutions using the differential inequality techniques are estimated.