论文标题
Fitzhugh-Nagumo方程中的浓度现象：一种介绍方法
Concentration phenomena in Fitzhugh-Nagumo's equations: A mesoscopic approach
论文作者
论文摘要
我们考虑一种具有强烈局部相互作用的空间扩展的介观菲茨ugh-nagumo模型，并证明其渐近极限会收敛于经典的非局部反应 - 反应 - 菲兹胡格·纳古莫系统。当局部相互作用强烈主导时，所考虑的介质方程的弱解决方案会收敛到局部平衡，该平衡的形式集中在平均膜电位上。我们的方法基于动力学理论（Wasserstein距离，相对熵法）中广泛发展的技术，其中将介质模型的宏观量与非局部反应扩散系统的解决方案进行了比较。这种方法允许在显微镜和反应扩散模型之间建立严格的联系。
We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong local interactions and prove that its asymptotic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. As the local interactions strongly dominate, the weak solution to the mesoscopic equation under consideration converges to the local equilibrium, which has the form of Dirac distribution concentrated to an averaged membrane potential. Our approach is based on techniques widely developed in kinetic theory (Wasserstein distance, relative entropy method), where macroscopic quantities of the mesoscopic model are compared with the solution to the nonlocal reaction-diffusion system. This approach allows to make the rigorous link between microscopic and reaction-diffusion models.
