On the global existence and finite time blow-up of shadow systems |
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| Authors: | Fang Li Wei-Ming Ni |
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| Affiliation: | a Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
b School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA |
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| Abstract: | 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. |
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| Keywords: | Shadow system Gierer-Meinhardt system Global existence Finite time blow-up |
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