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arXiv · 2502.13906

Multi-spots Steady States in Two-species Keller-Segel Models with Logistic Growth: Large Chemotactic Attraction Regime

Fanze Kong·Juncheng Wei·Liangshun Xu
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Abstract

One of the most important findings in the study of chemotactic process is self-organized cellular aggregation, and a high volume of results are devoted to the analysis of a concentration of single species. Whereas, the multi-species case is not understood as well as the single species one. In this paper, we consider two-species chemotaxis systems with logistic source in a bounded domain $\Omega\subset \mathbb R^2.$ Under the large chemo-attractive coefficients and one certain type of chemical production coefficient matrices, we employ the inner-outer gluing approach to construct multi-spots steady states, in which the profiles of cellular densities have strong connections with the entire solutions to Liouville systems and their locations are determined in terms of reduced-wave Green's functions. In particular, some numerical simulations and formal analysis are performed to support our rigorous studies.

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Fanze Kong, Juncheng Wei, Liangshun Xu. 2025-02-19. Multi-spots Steady States in Two-species Keller-Segel Models with Logistic Growth: Large Chemotactic Attraction Regime. https://arxiv.org/abs/2502.13906

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