American Institute of Mathematical Sciences

Advanced
July  2011, 16(1): 189-196. doi: 10.3934/dcdsb.2011.16.189

Travelling waves of a reaction-diffusion model for the acidic nitrate-ferroin reaction

Sheng-Chen Fu 1,

1. 

Department of Mathematical Sciences, National Chengchi University, 64, S-2 Zhi-nan Road, Taipei 116, Taiwan

Received  February 2010 Revised  July 2010 Published  April 2011

In this paper we consider a reaction-diffusion system which describes the acidic nitrate-ferroin reaction. We first show that there exists a minimum speed travelling wave solution. Then some estimates of the minimum speed(s) are derived. Finally, we find that the set of admissible wave speed is $[c_{m i n},\infty)$ under certain condition.
Keywords: travelling wave, Reaction-diffusion system, acidic nitrate-ferroin reaction..
Mathematics Subject Classification: Primary: 35K40; Secondary: 34A34, 35Q80, 35K5.
Citation: Sheng-Chen Fu. Travelling waves of a reaction-diffusion model for the acidic nitrate-ferroin reaction. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 189-196. doi: 10.3934/dcdsb.2011.16.189
References:
[1]

X. Chen and Y. Qi, Sharp estimates on minimum travelling wave speed of reaction diffusion systems modelling autocatalysis,, SIAM. J. Math. Anal., 39 (2007), 437.  doi: 10.1137/060665749.  Google Scholar

[2]

A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Etude de l'quation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique,, Moscow Univ. Bull. Math., 1 (1937), 1.   Google Scholar

[3]

I. Lengyel, G. Pota and G. Bazsa, Wave profile in the acidic nitrate-ferroin reaction,, J. Chem. Soc. Faraday Trans., 87 (1991), 3613.  doi: 10.1039/ft9918703613.  Google Scholar

[4]

J. H. Merkin and M. A. Sadiq, Reaction-diffusion travelling waves in the acidic nitrate-ferroin reaction,, J. Math. Chem., 17 (1995), 357.  doi: 10.1007/BF01165755.  Google Scholar

[5]

G. Pota, I. Lengyel and G. Bazsa, Travelling waves in the acidic nitrate-ferroin reaction,, J. Chem. Soc. Faraday Trans., 85 (1989), 3871.  doi: 10.1039/f19898503871.  Google Scholar

[6]

G. Pota, I. Lengyel and G. Bazsa, Travelling waves in the acidic nitrate-iron(II) reaction: Analytical description of the wave velocity,, J. Phys. Chem., 95 (1991), 4379.  doi: 10.1021/j100164a039.  Google Scholar

show all references

References:
[1]

X. Chen and Y. Qi, Sharp estimates on minimum travelling wave speed of reaction diffusion systems modelling autocatalysis,, SIAM. J. Math. Anal., 39 (2007), 437.  doi: 10.1137/060665749.  Google Scholar

[2]

A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Etude de l'quation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique,, Moscow Univ. Bull. Math., 1 (1937), 1.   Google Scholar

[3]

I. Lengyel, G. Pota and G. Bazsa, Wave profile in the acidic nitrate-ferroin reaction,, J. Chem. Soc. Faraday Trans., 87 (1991), 3613.  doi: 10.1039/ft9918703613.  Google Scholar

[4]

J. H. Merkin and M. A. Sadiq, Reaction-diffusion travelling waves in the acidic nitrate-ferroin reaction,, J. Math. Chem., 17 (1995), 357.  doi: 10.1007/BF01165755.  Google Scholar

[5]

G. Pota, I. Lengyel and G. Bazsa, Travelling waves in the acidic nitrate-ferroin reaction,, J. Chem. Soc. Faraday Trans., 85 (1989), 3871.  doi: 10.1039/f19898503871.  Google Scholar

[6]

G. Pota, I. Lengyel and G. Bazsa, Travelling waves in the acidic nitrate-iron(II) reaction: Analytical description of the wave velocity,, J. Phys. Chem., 95 (1991), 4379.  doi: 10.1021/j100164a039.  Google Scholar

[1]

Sheng-Chen Fu, Je-Chiang Tsai. Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4041-4069. doi: 10.3934/dcds.2013.33.4041
[2]

Tiberiu Harko, Man Kwong Mak. Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: An Abel equation based approach. Mathematical Biosciences & Engineering, 2015, 12 (1) : 41-69. doi: 10.3934/mbe.2015.12.41
[3]

Wei Wang, Wanbiao Ma. Global dynamics and travelling wave solutions for a class of non-cooperative reaction-diffusion systems with nonlocal infections. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3213-3235. doi: 10.3934/dcdsb.2018242
[4]

C. van der Mee, Stella Vernier Piro. Travelling waves for solid-gas reaction-diffusion systems. Conference Publications, 2003, 2003 (Special) : 872-879. doi: 10.3934/proc.2003.2003.872
[5]

H. J. Hupkes, L. Morelli. Travelling corners for spatially discrete reaction-diffusion systems. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1609-1667. doi: 10.3934/cpaa.2020058
[6]

Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631
[7]

Jifa Jiang, Junping Shi. Dynamics of a reaction-diffusion system of autocatalytic chemical reaction. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 245-258. doi: 10.3934/dcds.2008.21.245
[8]

Vladimir V. Chepyzhov, Mark I. Vishik. Trajectory attractor for reaction-diffusion system with diffusion coefficient vanishing in time. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1493-1509. doi: 10.3934/dcds.2010.27.1493
[9]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189
[10]

Jiang Liu, Xiaohui Shang, Zengji Du. Traveling wave solutions of a reaction-diffusion predator-prey model. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1063-1078. doi: 10.3934/dcdss.2017057
[11]

Bang-Sheng Han, Zhi-Cheng Wang. Traveling wave solutions in a nonlocal reaction-diffusion population model. Communications on Pure & Applied Analysis, 2016, 15 (3) : 1057-1076. doi: 10.3934/cpaa.2016.15.1057
[12]

Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2020001
[13]

Yong Jung Kim, Wei-Ming Ni, Masaharu Taniguchi. Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3707-3718. doi: 10.3934/dcds.2013.33.3707
[14]

Yuzo Hosono. Phase plane analysis of travelling waves for higher order autocatalytic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 115-125. doi: 10.3934/dcdsb.2007.8.115
[15]

Sze-Bi Hsu, Junping Shi, Feng-Bin Wang. Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3169-3189. doi: 10.3934/dcdsb.2014.19.3169
[16]

Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227-238. doi: 10.3934/mbe.2005.2.227
[17]

W. E. Fitzgibbon, M. Langlais, J.J. Morgan. A reaction-diffusion system modeling direct and indirect transmission of diseases. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 893-910. doi: 10.3934/dcdsb.2004.4.893
[18]

José-Francisco Rodrigues, Lisa Santos. On a constrained reaction-diffusion system related to multiphase problems. Discrete & Continuous Dynamical Systems - A, 2009, 25 (1) : 299-319. doi: 10.3934/dcds.2009.25.299
[19]

Haomin Huang, Mingxin Wang. The reaction-diffusion system for an SIR epidemic model with a free boundary. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2039-2050. doi: 10.3934/dcdsb.2015.20.2039
[20]

Sebastian Aniţa, Vincenzo Capasso. Stabilization of a reaction-diffusion system modelling malaria transmission. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1673-1684. doi: 10.3934/dcdsb.2012.17.1673

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences