Shadow systems are often used to approximate reaction-diffusion systems when one of the diffusion rates is large. In this paper, we study the global existence and blow-up phenomena for shadow systems. Our results show that even for these fundamental aspects, there are serious discrepancies between the dynamics of the reaction-diffusion systems and that of their corresponding shadow systems.
Bibliographical noteFunding Information:
Research supported in part by NSF. Part of the research presented here was done while the second author was visiting East China Normal University under the “111-project”. He wishes to thank the Mathematics Department and Professor Feng Zhou at ECNU for the warm hospitality and generous support. The authors also wish to express their gratitude to Professor Bei Hu for his helpful remarks concerning the work .
Copyright 2009 Elsevier B.V., All rights reserved.
- Finite time blow-up
- Gierer-Meinhardt system
- Global existence
- Shadow system