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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), 437-448. 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), 1-25. 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), 3613-3615. 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), 357-375. 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), 3871-3877. 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), 4379-4381. 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), 437-448. 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), 1-25. 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), 3613-3615. 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), 357-375. 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), 3871-3877. 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), 4379-4381. doi: 10.1021/j100164a039.  Google Scholar

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