MR2867015
Kanako SUZUKI and Izumi TAKAGI
Kanako SUZUKI and Izumi TAKAGI
On the Role of Basic Production Terms in an Activator-Inhibitor System Modeling Biological Pattern Formation
Funkcialaj Ekvacioj. Serio Internacia
54
2011
237--274
http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-2/54_237.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2867015
Considered is the asymptotic behavior of solutions to a class of reaction-diffusion systems comprised of an activator and an inhibitor, which includes the system proposed by Gierer and Meinhardt as a model of biological pattern formation. By the basic production terms we mean those independent of the unknown functions. We prove that, when the basic production term for the activator is absent, some solutions with large initial data converge to the trivial state, i.e., the activator vanishes identically. Also, we demonstrate that there exist solutions which start from large initial data and converge to a small stationary solution in the case where the basic production term for the inhibitor is nontrivial and that for the activator is sufficiently small.
Activator-inhibitor system, Pattern formation, Collapse of patterns, Steady-state patterns.
35K50, 35K57, 92C15.
54-237
2011
On the Role of Basic Production Terms in an Activator-Inhibitor System Modeling Biological Pattern Formation
Kanako SUZUKI and Izumi TAKAGI
Kanako SUZUKI and Izumi TAKAGI
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