带Michaelis-Menten型产出项的肿瘤浸润模型

Analysis of a signal production term of the Michaelis-Menten type modeling cancer invasion

考虑一个带Michaelis-Menten型信号产出项的趋化-趋触系统,该系统被用来刻画癌症浸润的过程.在初始数据是充分光滑的情况之下,证明该系统存在惟一且有界的整体光滑解.该模型由3个反应-扩散-偏微分方程组成,描述了肿瘤细胞、基质降解酶、细胞外基质的变化.首先,对该模型用偏微分方程原理来加以分析研究,利用压缩不动点定理证明了系统局部解的存在性和惟一性,然后在初始数据充分光滑的前提下,证明该系统存在惟一且有界的整体光滑解.

A chemotaxis-haptotaxis model with a signal production term of the Michaelis-Menten type was contained.This system can be used to describe the process of caner invasion.The model consists of a 3×3reaction-diffusion-taxis partial differential equations describing interactions between cancer cells,matrix degrading enzymes,and the host tissue,and it includes two bounded nonlinear density-dependent chemotactic and haptotactic sensitivity functions.The model is analyzed by the theory of partial differential equations.The local existence and uniqueness of solutions is first proved by the fixed point theorem.Then,Under the assumption that the initial data is sufficiently smooth.This system admits a unique global smooth solution that is uniformly bounded.