A free boundary problem in a singular limit of a three-component reaction-diffusion system (Mathematical and numerical analysis for interface motion arising in nonlinear phenomena)
Hideki Murakawa, Hirokazu Ninomiya · Institutional Repositories DataBase (IRDB) · 2012
We consider a three-component reaction-diffusion system with a reaction rate parameter, and investigate its singular limit as the reaction rate tends to infinity.The limit problem is described by a nonlinear cross-diffusion system.The system is regarded as a weak form of a free boundary problem which possesses three types of free boundaries.Triple junction points appear at the intersection of the three interfaces.Furthermore, the dynamics is governed by a system of equations in each region separated by the free boundaries.A linear numerical scheme for capturing the interfaces is introduced and numerical simulations are carried out to demonstrate our theoretical results. §1. IntroductionWe are interested in asymptotic behavior of solutions of reaction-diffusion systems.Especially, we are studying a kind of singular limit problems, which is called fast reaction limit.In this paper, we deal with fast reaction limit of the following three-component