AI 中文总结
本文针对具有双依赖迁移率的三组分反应-扩散系统，通过分类讨论建立其经典解的全局存在性、有界性与渐近行为，揭示该迁移率函数对系统长期行为的关键影响。
AI 中文摘要
本文研究具有双依赖迁移率的三组分反应-扩散系统的初边值问题，该迁移率同时依赖于化学浓度和营养水平。我们通过分类讨论并利用迁移率函数的特定结构性质，系统建立了该系统在无通量边界条件下经典解的全局存在性、有界性与渐近行为。通过对比不同情形下的结果，我们证明解会收敛到不同的常数稳态，从而表明双依赖迁移率函数对系统的长期行为具有关键作用。
英文摘要
In this paper, we consider the initial-boundary value problem of a three-component reaction-diffusion system with dual-dependent motility, which depends on both the chemical concentration and the nutrient level. We systematically establish the global existence, boundedness, and asymptotic behavior of the classical solutions to the system with no-flux boundary conditions through classified discussion and by exploiting specific structural properties of the motility function. In turn, by comparing the results obtained in the distinct cases, we demonstrate that the solution converges to different constant steady states, thereby indicating the crucial role of the dual-dependent motility function in the long-term behavior of the system.
