格动力系统中的模式形成问题

In this program, it is studied that the existence of global attractors and its Hausdorff dimension for some lattice differential equations and coupled map lattices which arised from spatially discreted and spatio-temporally discreted FitzHugh-Nagumo equations, and the existence of traveling wave solution for reaction diffusion systems with time delay and delayed lattice dynamical systems. The viscosity solutions to fully nonlinear elliptic and parabolic systems and parabolic functional-differential equationsare also studied.

本项目研究格动力系统的模式形成问题，内容包括空间离散反应扩散方程的全局吸引子及其性质、格动力系统的行波解及其分支和稳定性，离散反应扩散方程的时空复杂性。研究方法以理论分析为主，并充分利用计算机开展计算和模拟。该项研究对常微分方程、反应扩散方程、映射、动力系统、计算数学有理论意义，对材料科学、图像处理等学科有应用意义。....