The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex nontrivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we apply the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results.

Keller-Segel模型是描述趋化机制的范式，对单细胞和多细胞生物的生理和病理活动起着至关重要的作用。最有趣的变体之一是具有内在增长的耦合系统，它允许许多复杂的非平凡模式。本文致力于构建具有二维逻辑源的 Keller-Segel 模型的多尖峰解。假设化学吸引率很大，我们将内外粘合方案应用于非局部交叉扩散系统，并证明了多个边界和内部尖峰的存在。数值模拟的提出是为了强调我们的理论结果。