基于非局部流的癌细胞浸润组织模型分析

Analyses on a Nonlocal Flux Model for Cancer Cell Invasion of Surrounding Tissue

带非局部黏附项的癌细胞浸润组织模型描述了癌症细胞、周围健康组织以及基质降解酶之间的相互作用,它是一个非局部的反应-扩散-对流方程组.在零流边界条件和对初始数据合适的假设下,证明了该模型存在唯一且有界的整体光滑解.进一步,证明了该整体解指数收敛到常数稳态解.

In the modeling of cancer cell invasion of the extracellular matrix,a nonlocal reaction-diffusion-advection model was recently proposed to describe the interactions between cancer cells,extracellular matrix and matrix degrading enzymes. Under no-flux boundary conditions and some appropriate assumptions on initial data,it was shown that the model possesses an unique global classical solution which is uniformly bounded. Furthermore,under the additional assumptions and some other technical assumptions,it was proved that any classical solution of the model approaches the spatially uniform state as the time goes to infinity.