TY - JOUR
T1 - Monotonicity of stable solutions in shadow systems
AU - Ni, Wei Ming
AU - Poläcik, Peter
AU - Yanagida, Eiji
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
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U2 - 10.1090/s0002-9947-01-02880-x
DO - 10.1090/s0002-9947-01-02880-x
M3 - Article
AN - SCOPUS:23044528996
SN - 0002-9947
VL - 353
SP - 5057
EP - 5069
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 12
ER -