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Mathematics > Analysis of PDEs

arXiv:1807.01832 (math)
[Submitted on 5 Jul 2018]

Title:Front propagation in both directions and coexistence of traveling fronts and pulses

Authors:Chao-Nien Chen, Y.S. Choi
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Abstract:For scalar reaction-diffusion equations, a traveling wave is a front which transforms a higher energy state to a lower energy state. The same is true for a system of equations with a gradient structure. At the core of this phenomenon, the wave propagation results in an invasion of an equilibrium state from a different one. This paper is aimed at two questions:
(i) Can reaction-diffusion waves exhibit front propagation in both directions between two distinct equilibrium states? (ii) The co-existence of traveling fronts and pulses; a subject rarely studied.
Working on a FitzHugh-Nagumo model with the same physical parameters, we give positive answers to both questions.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1807.01832 [math.AP]
  (or arXiv:1807.01832v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1807.01832

Submission history

From: Yung Choi [view email]
[v1] Thu, 5 Jul 2018 03:07:17 UTC (90 KB)
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