Monotonicity of stable solutions in shadow systems

Wei Ming Ni, Peter Poläcik, Eiji Yanagida

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


A shadow system appears as a limit of a reaction-diffusion system in which some components have infinite diffusivity. We investigate the spatial structure of its stable solutions. It is known that, unlike scalar reactiondiffusion equations, some shadow systems may have stable nonconstant (monotone) solutions. On the other hand, it is also known that in autonomous shadow systems any nonconstant non-monotone stationary solution is necessarily unstable. In this paper, it is shown in a general setting that any stable bounded (not necessarily stationary) solution is asymptotically homogeneous or eventually monotone in x.

Original languageEnglish (US)
Pages (from-to)5057-5069
Number of pages13
JournalTransactions of the American Mathematical Society
Issue number12
StatePublished - 2001
Externally publishedYes


Dive into the research topics of 'Monotonicity of stable solutions in shadow systems'. Together they form a unique fingerprint.

Cite this