AI 中文总结
研究全空间中具有退化扩散的双物种趋化系统，通过精细能量估计建立弱解全局存在性，在参数额外假设下得出解向常数稳态的指数收敛速率，揭示强退化扩散确保全局有界性和指数稳定性。
AI 中文摘要
本文研究了全空间\(\R^d(d \ge 3)\)中具有退化扩散的双物种趋化系统。每个物种的扩散由多孔介质型算子控制。在扩散和聚集指数的适当条件下，建立了一致有界弱解的全局存在性。证明依赖于精细的能量估计，利用退化扩散的正则化效应抵消趋化聚集。此外，在系统参数的额外假设下，得出解向常数稳态的指数收敛速率。结果表明足够强的退化扩散确保全空间的全局有界性和指数稳定性。
英文摘要
This paper investigates a two-species chemotaxis system with degenerate diffusion in the whole space $\R^d(d \ge 3)$. The diffusion of each species is governed by porous-medium-type operators. Under suitable conditions on the diffusion and aggregation exponents, we establish the global existence of uniformly bounded weak solutions. The proof hinges on a refined energy estimate that exploits the regularizing effect of degenerate diffusion to counteract the chemotactic aggregation. Furthermore, under additional assumptions on the system parameters, we derive exponential convergence rates of the solutions toward the constant steady state. Our results reveal that sufficiently strong degenerate diffusion ensures global boundedness and exponential stabilization in the whole space.
