TY - JOUR
T1 - Highly oscillatory behavior of the activator in the Gierer and Meinhardt system
AU - Felmer, Patricio
AU - Martínez, Salomé
AU - Tanaka, Kazunaga
PY - 2008/4
Y1 - 2008/4
N2 - In this article we construct a new type of solutions for the Gierer and Meinhardt system -ε2uxx + u &=&u 2/v in (0,L),- vxx+ v &=& u2 in (0, L) with boundary conditions u x (0) = u x (L) = 0 and v x (0) = v x (L) = 0. As ε approaches zero, we construct a family of positive solution (u ε , v ε ) such that the activator u ε oscillates c 0/ε times, with c 0 in an appropriate range, while the inhibitor remains close to a limiting profile, which is a strictly decreasing function.
AB - In this article we construct a new type of solutions for the Gierer and Meinhardt system -ε2uxx + u &=&u 2/v in (0,L),- vxx+ v &=& u2 in (0, L) with boundary conditions u x (0) = u x (L) = 0 and v x (0) = v x (L) = 0. As ε approaches zero, we construct a family of positive solution (u ε , v ε ) such that the activator u ε oscillates c 0/ε times, with c 0 in an appropriate range, while the inhibitor remains close to a limiting profile, which is a strictly decreasing function.
UR - http://www.scopus.com/inward/record.url?scp=38549129168&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38549129168&partnerID=8YFLogxK
U2 - 10.1007/s00208-007-0167-2
DO - 10.1007/s00208-007-0167-2
M3 - Article
AN - SCOPUS:38549129168
SN - 0025-5831
VL - 340
SP - 749
EP - 773
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 4
ER -