论文标题
在具有信号依赖性动力的抛物线纤维素凯勒 - 塞格系统上：全球界限和稳态的范式
On the parabolic-elliptic Keller-Segel system with signal-dependent motilities: a paradigm for global boundedness and steady states
论文作者
论文摘要
本文涉及抛物线纤维素的凯勒 - 塞格系统，该系统均具有扩散和趋化系数（运动函数）取决于化学信号密度。该系统最初是由Keller和Segel在\ cite {KS-1971-JTB2}中提出的，以描述{\ it dictyostelium discoideum}细胞的聚集阶段，以响应于分泌的化学信号循环腺苷单磷酸盐（CAMP），但可用的分析结果非常有限。考虑系统在具有Neumann边界条件的有界平滑域中的系统，我们在任何维度上建立了在信号依赖性运动函数上具有适当一般条件的任何维度的全局界限，这些函数适用于广泛的运动函数。研究了非恒定稳态的存在/不存在，并发现了丰富的固定曲线。概述了一些开放问题，以供进一步追求。我们的结果表明，具有信号依赖性运动的Keller-segel系统的固定溶液的全局界限和概况取决于运动功能，空间维度的衰减速率以及扩散性和趋化性运动之间的关系，这使动力学变得非常丰富。
This paper is concerned with a parabolic-elliptic Keller-Segel system where both diffusive and chemotactic coefficients (motility functions) depend on the chemical signal density. This system was originally proposed by Keller and Segel in \cite{KS-1971-JTB2} to describe the aggregation phase of {\it Dictyostelium discoideum} cells in response to the secreted chemical signal cyclic adenosine monophosphate (cAMP), but the available analytical results are very limited by far. Considering system in a bounded smooth domain with Neumann boundary conditions, we establish the global boundedness of solutions in any dimensions with suitable general conditions on the signal-dependent motility functions, which are applicable to a wide class of motility functions. The existence/nonexistence of non-constant steady states is studied and abundant stationary profiles are found. Some open questions are outlined for further pursues. Our results demonstrate that the global boundedness and profile of stationary solutions to the Keller-Segel system with signal-dependent motilities depend on the decay rates of motility functions, space dimensions and the relation between the diffusive and chemotactic motilities, which makes the dynamics immensely wealthy.
