TY - JOUR
T1 - Existence of pulses in excitable media with nonlocal coupling
AU - Faye, Grégory
AU - Scheel, Arnd
N1 - Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2015/1/2
Y1 - 2015/1/2
N2 - We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with finite-range, non-local coupling. Our approach replaces methods from geometric singular perturbation theory, that had been crucial in previous existence proofs, by a PDE oriented approach, relying on exponential weights, Fredholm theory, and commutator estimates.
AB - We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with finite-range, non-local coupling. Our approach replaces methods from geometric singular perturbation theory, that had been crucial in previous existence proofs, by a PDE oriented approach, relying on exponential weights, Fredholm theory, and commutator estimates.
KW - FitzHugh-Nagumo system
KW - Fredholm operators
KW - Nonlocal equation
KW - Traveling wave
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U2 - 10.1016/j.aim.2014.11.005
DO - 10.1016/j.aim.2014.11.005
M3 - Article
AN - SCOPUS:84911941556
SN - 0001-8708
VL - 270
SP - 400
EP - 456
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -