Traveling wave to a reaction-hyperbolic system for axonal transport

被引：0
|
作者：
Huang, Feimin [1 ,2 ]
Li, Xing [3 ]
Zhang, Yinglong [4 ]
机构：
[1] Hunan Normal Univ, Coll Math & Comp Sci, Changsha, Hunan, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
[3] Shenzhen Univ, Coll Math & Stat, Shenzhen, Peoples R China
[4] Seoul Natl Univ, Dept Math Sci, Seoul, South Korea
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 01期
关键词：
Reaction-hyperbolic system; Axonal transport; Traveling wave; Convergence rate; CONSERVATION-LAWS; CONVERGENCE; RELAXATION; ORGANELLES; EQUATIONS; ENTROPY; MOTION;
D O I：
10.1016/j.jde.2017.02.033
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 n x n (n >= 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. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：264 / 284
页数：21
相关论文
共 50 条
  • [41] TRAVELING WAVE SOLUTIONS FOR A CHEMOTAXIS SYSTEM
    Catrina, F.
    Reyes, V. M. G.
    [J]. BIOMAT 2013: INTERNATIONAL SYMPOSIUM ON MATHEMATICAL AND COMPUTATIONAL BIOLOGY, 2014, : 43 - 62
  • [42] Traveling wave fault location system
    Dai, Wenjin
    Fang, Min
    Cui, Lizhen
    [J]. WCICA 2006: SIXTH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION, VOLS 1-12, CONFERENCE PROCEEDINGS, 2006, : 7449 - 7452
  • [43] TRAVELING WAVE SOLUTIONS TO A GRADIENT SYSTEM
    REINECK, JF
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 307 (02) : 535 - 544
  • [44] THE EXISTENCE OF TRAVELING WAVE FRONTS FOR A REACTION-DIFFUSION SYSTEM MODELLING THE ACIDIC NITRATE-FERROIN REACTION
    Fu, Sheng-Chen
    [J]. QUARTERLY OF APPLIED MATHEMATICS, 2014, 72 (04) : 649 - 664
  • [45] Traveling wave transport of particles and particle size classification
    Kawamoto, H
    Hasegawa, N
    Seki, K
    [J]. IS&T'S NIP19: INTERNATIONAL CONFERENCE ON DIGITAL PRINTING TECHNOLOGIES, 2003, : 100 - 106
  • [46] Traveling wave transport of particles and particle size classification
    Kawamoto, H
    Hasegawa, N
    [J]. JOURNAL OF IMAGING SCIENCE AND TECHNOLOGY, 2004, 48 (05) : 404 - 411
  • [47] Traveling wave ion transport for the cyclotron gas stopper
    Brodeur, M.
    Joshi, N.
    Gehring, A. E.
    Bollen, G.
    Morrissey, D. J.
    Schwarz, S.
    [J]. NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION B-BEAM INTERACTIONS WITH MATERIALS AND ATOMS, 2013, 317 : 468 - 472
  • [48] STABILITY OF TRAVELING WAVE SOLUTIONS TO CAUCHY PROBLEM OF DIAGNOLIZABLE QUASILINEAR HYPERBOLIC SYSTEMS
    Liu, Cunming
    Liu, Jianli
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (11) : 4735 - 4749
  • [49] Traveling wave solutions of a nonlinear reaction–advection equation
    Konstadia Lika
    Thomas G. Hallam
    [J]. Journal of Mathematical Biology, 1999, 38 : 346 - 358
  • [50] SOME TRAVELING WAVE REACTION DIFFUSION-PROBLEMS
    BORZI, C
    FRISCH, HL
    GIANOTTI, R
    PERCUS, JK
    [J]. RADIATION EFFECTS AND DEFECTS IN SOLIDS, 1989, 112 (1-2): : 119 - 123
12345