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Abstract and Applied Analysis
Volume 2012, Article ID 735675, 9 pages
http://dx.doi.org/10.1155/2012/735675
Research Article

Monostable-Type Travelling Wave Solutions of the Diffusive FitzHugh-Nagumo-Type System in 𝐑 𝑁

Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan

Received 30 March 2012; Accepted 25 May 2012

Academic Editor: Norimichi Hirano

Copyright © 2012 Chih-Chiang Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with monostable-type travelling wave solutions of the diffusive FitzHugh-Nagumo-type system (FHN) in 𝐑 𝑁 for the two components 𝑢 and 𝑣 . By solving 𝑣 in terms of 𝑢 , this system can be reduced to a nonlocal single equation for 𝑢 . When the diffusion coefficients in the system are equal, we construct travelling wave solutions for the non-local equation by the method of super- and subsolutions developed by Morita and Ninomiya (2008) Moreover, we propose a condition for 𝛾 , which is similar to the condition Reinecke and Sweers (1999) used to transform (FHN) into a quasimonotone system.