On the global existence and finite time blow-up of shadow systems

Fang Li, Wei Ming Ni

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23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1762-1776
Number of pages15
JournalJournal of Differential Equations
Issue number6
StatePublished - Sep 15 2009

Bibliographical note

Funding 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 [7].


  • Finite time blow-up
  • Gierer-Meinhardt system
  • Global existence
  • Shadow system


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