PDE Seminar (2015/5/25): Fast reaction limit of a PDE-ODE type reaction-diffusion system with different reaction terms

Date
2015-5-25 16:30 - 2015-5-25 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Harunori Monobe (Meiji University)
 
We consider a kind of singular limit problems, which is called fast reaction limit. The problem of fast reaction limit is to study behaviors of solutions of reaction diffusion systems when those reaction speeds are very fast. The fast reaction limits of two-component systems have been studied for the past few decades. In each system, reaction terms were represented by the same function. For instance, Hilhorst, van der Hout and Peletier (1996) considered a simple two-component system with a common reaction term and showed that the fast reaction limit of the system is written as the one-phase Stefan problem.

In this talk, we investigate a PDE-ODE type reaction-diffusion system of which reaction terms consist of power functions with different powers. Free boundaries appear in fast reaction limit of the system. Behaviors of the interfaces are examined. We have three types of behaviors depending on the powers: (i) the initial interface vanishes instantaneously, (ii) the interface propagates in finite speed, and (iii) the interface does not move. This talk is based on the joint work with Masato Iida, Hideki Murakawa and Hirokazu Ninomiya.