一类模拟血管生成的双曲-抛物耦合方程解的性态研究

血管生成是由内皮细胞的产物诱发，在趋化环境中发生的血管形成过程，其反应机制可以用一类双曲——抛物方程，也称PEC模型来模拟。本项目拟围绕三维PEC模型常状态附近线性扩散波的稳定性和最优衰减、一维PEC模型非线性扩散波的稳定性和衰减率、三维PEC模型平面扩散波的稳定性和衰减率以及有界域中非平凡稳态解附近光滑解的存在性和衰减率等问题展开系统深入的研究。本项目的顺利进行必将丰富PEC模型的数学理论，期望对解释某些生物现象提供重要的参考。

Vasculogenesis is the process of blood vessel formation occurring by the production of endothelial cells and is lead by a chemotactic phenomenon, i.e., cells direct their movement according to certain chemicals in their environment. The reaction mechanism can be simulated by a hyperbolic-parabolic model, also known as PEC model. In this project, we are concerned with the stability and the optimal decay rates of linear diffusion wave on three dimensional PEC model, nonlinear diffusion wave on one-dimensional PEC model, planar diffusion waves on three dimensional PEC model when initial data are different at far fields and the existence and decay rates of solutions to the three dimensional PEC model on a bounded domain. The progress of this project will enrich the mathematical theory of the PEC model, and it is expected to provide an important reference for the interpretation of certain biological phenomena.