【摘要】 该文基于几何奇异摄动理论的降维方法,结合旋转向量场和相平面分析等工具,研究了一类考虑Allee效应的用于描述社会张力-动荡演化多尺度反应-扩散系统的波前解的存在性.在三种不同的极限假设下,得到了不同的降维方式并基于低维系统的异宿连接,分别得到上述系统连接不同稳态解的波前解的存在性.更多还原

【Abstract】 Based on the geometric singular perturbation theory,and combining with the tools of generalized rotating vector field and phase plane analysis,this paper studies the existence of traveling fronts for a class of multi-scale reaction-diffusion system describing social tension-outbursts with Allee effect.Under three different limiting assumptions on scales,we obtain three different dimensionreduction settings to get the low-dimensional systems processing heteroclinic connections.Thus,we obtain the existence of traveling fronts connecting different steady-state solutions of the multi-scale reaction-diffusion system mentioned-above.更多还原