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

作　　者：张娜[1] 雷梁[2] 

机构地区：[1]河南城建学院计算机科学与工程系,河南平顶山467036 [2]信阳师范学院计算机与信息技术学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2015年第3期326-330,共5页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(61202248)

摘　　要：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.

关 键 词：非局部流 黏附 整体存在性 有界性 渐近行为 

分 类 号：O175.26[理学—数学]