Existence of pulses in excitable media with nonlocal coupling |
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Authors: | Gré gory Faye,Arnd Scheel |
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Affiliation: | University of Minnesota, School of Mathematics, 206 Church Street S.E., Minneapolis, MN 55455, USA |
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Abstract: | 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. |
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Keywords: | Traveling wave Nonlocal equation FitzHugh&ndash Nagumo system Fredholm operators |
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