Speaker: Professor Hirokazu Ninomiya, Meiji University, Japan
Title: Propagation phenomena in reaction-diffusion equations
Propagation phenomena arise in a large variety of systems in physics, chemistry and biology. In this talk we focus on propagation phenomena of reaction-diffusion equations. Recently traveling wave solutions and entire solutions of reaction-diffusion equations have been intensively studied. Here a traveling wave solution means a solution translating with a constant speed without changing its profile and an entire solution is a solution existing for any positive and negative time. Various traveling wave solutions and entire solutions have been constructed not only in the whole space, but also in an exterior domain. I will survey the recent studies and the relation between traveling wave solutions and the entire solutions. For the exterior domain, I will also explain the influence of the shape of the domain. Finally I will explain the propagation on excitable media which is related to ventricular fibrillation.