Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774088 | Journal of Differential Equations | 2017 | 21 Pages |
Abstract
In this paper, we study a class of nonlinear reaction-hyperbolic systems modeling the neuronal signal transfer in neuroscience. This reaction-hyperbolic system can be regarded as nÃn (nâ¥2) hyperbolic system with relaxation. We first prove the existence of traveling wave by Gershgorin circle theorem and mathematically describe the neuronal signal transport. Then for a special case n=2, we show the traveling wave is nonlinearly stable, and obtain the convergence rate simultaneously by a weighted estimate.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Feimin Huang, Xing Li, Yinglong Zhang,