Blow-up and Lower Bounds of Solutions to a Two-Species Keller-Segel Chemotaxis Model in $\mathbb{R}^2$
DOI:
https://doi.org/10.5890/JAND.2026.03.006Abstract
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 $\Omega\subset\mathbb{R}^2$ with smooth boundary. We establish the results for the finite time blow-up of solutions when $\frac{\chi_1}{\alpha}=\frac{\chi_2}{\beta}$ for some positive constants $\alpha$ and $\beta$. 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.References
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