Reaction-diffusion approximation
Prof. Hirokazu NinomiyaMeiji University, Japan 下午 3:30–5:00 鴻經館 107 室Abstract：
A reaction-diffusion system consists of kinetic term and diffusion term.Diffusion homogenizes a solution. It looks a simple equation. However, a pattern of solution sometimes performs by combing a kinetic effect, which is called Turing’s instability. In this talk, I will explain that the reaction-diffusion systems are close to the other types of partial differential equations by using the singular perturbation method. Indeed, I will present three types of approximations: cross-diffusion systems, non-local evolutionary equations with any even kernels, semi linear wave equation by reaction-diffusion systems. In some cases, the pattern formation by cross-diffusivity or the nonlocal term can be explained by Turing’s instability through the reaction-diffusion approximation.