TY - JOUR
T1 - On the Structure of Multiple Existence of Stable Stationary Solutions in Systems of Reaction-Diffusion Equations
AU - Fujii, Hiroshi
AU - Nishiura, Yasumasa
AU - Hosono, Yuzo
PY - 1986
Y1 - 1986
N2 - This article is intended to survey the results about pattern formation in a class of reaction-diffusion systems. The focus is on the phenomenon of multiple existence of stable stationary solutions, which has biologically or physically significant consequences. The mathematical structure and stability of stationary solutions is investigated in a certain parameter space. Especially, σ-local stability and instability theorems for D1-sheet are given, and stabilization of D2-sheet is proved via two approaches: the spectral method and the singular perturbation-theoretic one.
AB - This article is intended to survey the results about pattern formation in a class of reaction-diffusion systems. The focus is on the phenomenon of multiple existence of stable stationary solutions, which has biologically or physically significant consequences. The mathematical structure and stability of stationary solutions is investigated in a certain parameter space. Especially, σ-local stability and instability theorems for D1-sheet are given, and stabilization of D2-sheet is proved via two approaches: the spectral method and the singular perturbation-theoretic one.
KW - bifurcation
KW - pattern formation
KW - reaction-diffusion
KW - singular perturbation
KW - stability
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U2 - 10.1016/S0168-2024(08)70131-0
DO - 10.1016/S0168-2024(08)70131-0
M3 - Article
AN - SCOPUS:77957080860
SN - 0168-2024
VL - 18
SP - 157
EP - 219
JO - Studies in Mathematics and its Applications
JF - Studies in Mathematics and its Applications
IS - C
ER -