Fast-reaction asymptotics for a time-dependent reaction-diffusion system with a growing nonlinear source term
TI Seidman, Adrian Muntean · TU/e Research Portal · 2010
In this paper, we prove rigorously the fast-reaction asymptotics lambda -> infinity for a reaction-diffusion system having a nonlinear production term with very rapid reaction rate lambda. We derive the limit PDE system and prove the uniqueness of its solutions. The key tools of our analysis include (uniform w.r.t. lambda) L^1-estimates for both q and w and a balanced formulation, where combinations of the original components which balance the fast reaction are used. The results reported here answer some open questions raised by T.I. Seidman in the paper [16].