Traveling waves in delayed reaction-diffusion equations in biology

Sergei Trofimchuk;  ; Vitaly Volpert;  ;  ;

doi:10.3934/mbe.2020339

Traveling waves in delayed reaction-diffusion equations in biology

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2020339 ◽

2020 ◽

Vol 17 (6) ◽

pp. 6487-6514

Author(s):

Sergei Trofimchuk ◽

◽

Vitaly Volpert ◽

◽

...

Keyword(s):

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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Erratum: Global Stability of Monostable Traveling Waves For Nonlocal Time-delayed Reaction-diffusion Equations

SIAM Journal on Mathematical Analysis ◽

10.1137/110850633 ◽

2012 ◽

Vol 44 (1) ◽

pp. 538-540 ◽

Cited By ~ 3

Author(s):

Ming Mei ◽

Chunhua Ou ◽

Xiao-Qiang Zhao

Keyword(s):

Global Stability ◽

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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Time-delayed reaction–diffusion equations with boundary effect: (I) convergence to non-critical traveling waves

Applicable Analysis ◽

10.1080/00036811.2016.1258696 ◽

2016 ◽

Vol 97 (2) ◽

pp. 230-254

Author(s):

Yicheng Jiang ◽

Kaijun Zhang

Keyword(s):

Traveling Waves ◽

Boundary Effect ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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On the existence of traveling waves for delayed reaction–diffusion equations

Journal of Differential Equations ◽

10.1016/j.jde.2009.04.002 ◽

2009 ◽

Vol 247 (3) ◽

pp. 887-905 ◽

Cited By ~ 38

Author(s):

Haiyan Wang

Keyword(s):

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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Global Asymptotic Stability of Traveling Waves in Delayed Reaction-Diffusion Equations

SIAM Journal on Mathematical Analysis ◽

10.1137/s0036141098346785 ◽

2000 ◽

Vol 31 (3) ◽

pp. 514-534 ◽

Cited By ~ 124

Author(s):

Hal L. Smith ◽

Xiao-Qiang Zhao

Keyword(s):

Asymptotic Stability ◽

Traveling Waves ◽

Global Asymptotic Stability ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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Perron Theorem in the monotone iteration method for traveling waves in delayed reaction–diffusion equations

Journal of Differential Equations ◽

10.1016/j.jde.2008.01.004 ◽

2008 ◽

Vol 244 (7) ◽

pp. 1551-1570 ◽

Cited By ~ 27

Author(s):

Amin Boumenir ◽

Van Minh Nguyen

Keyword(s):

Traveling Waves ◽

Iteration Method ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction ◽

Monotone Iteration

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Stability of traveling waves for nonlocal time-delayed reaction-diffusion equations

Kinetic and Related Models ◽

10.3934/krm.2018048 ◽

2018 ◽

Vol 11 (5) ◽

pp. 1235-1253

Author(s):

Yicheng Jiang ◽

◽

Kaijun Zhang

Keyword(s):

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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Uniqueness of non-monotone traveling waves for delayed reaction-diffusion equations

Applied Mathematics Letters ◽

10.1016/j.aml.2009.01.014 ◽

2009 ◽

Vol 22 (7) ◽

pp. 1056-1061 ◽

Cited By ~ 15

Author(s):

Shi-Liang Wu ◽

San-Yang Liu

Keyword(s):

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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Global Stability of Monostable Traveling Waves For Nonlocal Time-Delayed Reaction-Diffusion Equations

SIAM Journal on Mathematical Analysis ◽

10.1137/090776342 ◽

2010 ◽

Vol 42 (6) ◽

pp. 2762-2790 ◽

Cited By ~ 63

Author(s):

Ming Mei ◽

Chunhua Ou ◽

Xiao-Qiang Zhao

Keyword(s):

Global Stability ◽

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

Download Full-text

Traveling waves for nonlocal and non-monotone delayed reaction-diffusion equations

Acta Mathematica Sinica English Series ◽

10.1007/s10114-013-1769-0 ◽

2013 ◽

Vol 29 (11) ◽

pp. 2159-2180 ◽

Cited By ~ 5

Author(s):

Zhi Ting Xu ◽

Pei Xuan Weng

Keyword(s):

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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Asymptotic stability of traveling waves for delayed reaction-diffusion equations with crossing-monostability

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-010-0112-1 ◽

2010 ◽

Vol 62 (3) ◽

pp. 377-397 ◽

Cited By ~ 23

Author(s):

Shi-Liang Wu ◽

Hai-Qin Zhao ◽

San-Yang Liu

Keyword(s):

Asymptotic Stability ◽

Traveling Waves ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Delayed Reaction

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