THE SUB-SUPERSOLUTION METHOD FOR THE FITZHUGH-NAGUMO TYPE REACTION-DIFFUSION SYSTEM WITH HETEROGENEITY

摘要

We construct a heteroclinic solution to the FitzHugh-Nagumo type reaction-diffusion system (FHN RD system) with heterogeneity by the sub-supersolution method due to [5]. sigma(d, gamma) is introduced as the Rayleigh quotient corresponding to a linearized eigenvalue problem of the subsolution, where d and gamma are parameters. The key to construct the solution is the uniform estimate for sigma(.,.) from below. In addition, it enables us to analyze an asymptotic behavior of the solution.