-
Previous Article
Heteroclinic limit cycles in competitive Kolmogorov systems
- DCDS Home
- This Issue
-
Next Article
The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation
Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction
1. | Department of Mathematical Sciences, National Chengchi University, 64, S-2 Zhi-nan Road, Taipei 116 |
2. | Department of Mathematics & AIM-HI, National Chung Cheng University, Chiayi, Taiwan |
References:
[1] |
K. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000. |
[2] |
P. C. Fife, "Mathematical Aspects of Reacting and Diffusing Systems," Lecture Notes in Biomathematics, 28, Springer-Verlag, Berlin, 1979. |
[3] |
S. Focant and Th. Gallay, Existence and stability of propagating fronts for an autocatalytic a reaction-diffusion system, Physica D, 120 (1998), 346-368.
doi: 10.1016/S0167-2789(98)00096-7. |
[4] |
S.-C. Fu, Travelling waves of a reaction-diffusion model for the acidic nitrate-ferroin reaction, Discrete Contin. Dyn. Syst., 16 (2011), 189-196.
doi: 10.3934/dcdsb.2011.16.189. |
[5] |
S.-C. Fu, The existence of traveling wave fronts for a reaction-diffusion system modelling the acidic nitrate-ferroin reaction, Quarterly Appl. Math., to appear. |
[6] |
I. Lengyel, G. Pota and G. Bazsa, Wave profile in the acidic nitrate-ferroin reaction, J. Chem. Soc. Faraday Trans., 87 (1991), 3613-3615. |
[7] |
Y. Li and Y. Wu, Stability of travelling waves with noncritical speeds for double degenerate Fisher-type equations, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), 149-170.
doi: 10.3934/dcdsb.2008.10.149. |
[8] |
Y. Li and Y. Wu, Stability of traveling front solutions with algebraic spatial decay for some autocatalytic chemical reaction systems, SIAM J. Math. Anal., 44 (2012), 1474-1521.
doi: 10.1137/100814974. |
[9] |
J. H. Merkin and M. A. Sadiq, Reaction-diffision travelling waves in the acidic nitrate-ferroin reaction, J. Math. Chem., 17 (1995), 357-375.
doi: 10.1007/BF01165755. |
[10] |
J. D. Murray, "Mathematical Biology. I. An Introduction," Springer-Verlag, New York, 2004. |
[11] |
A. Pazy, "Semigroup of Linear Operators and Applications to Partial Differential Equations," Springer-Verlag, Berling, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[12] |
R. L. Pego and M. I. Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys., 164 (1994), 305-349. |
[13] |
G. Pota, I. Lengyel and G. Bazsa, Travelling waves in the acidic nitrate-ferroin reaction, J. Chem. Soc. Faraday Trans., 85 (1989), 3871-3877. |
[14] |
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. |
[15] |
G. Raugel and K. Kirchgässner, Stability of fronts for a KPP-system. II. The critical case, J. Differential Equations, 146 (1998), 399-456.
doi: 10.1006/jdeq.1997.3391. |
[16] |
Y. Wu, X. Xing and Q. Ye, Stability of travelling waves with algebraic decay for n-degree Fisher-type equations, Discrete Contin. Dyn. Syst., 16 (2006), 47-66.
doi: 10.3934/dcds.2006.16.47. |
[17] |
Y. Wu and X. Xing, Stability of traveling waves with critical speeds for p-degree Fisher-type equations, Discrete Contin. Dyn. Syst., 20 (2008), 1123-1139.
doi: 10.3934/dcds.2008.20.1123. |
show all references
References:
[1] |
K. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000. |
[2] |
P. C. Fife, "Mathematical Aspects of Reacting and Diffusing Systems," Lecture Notes in Biomathematics, 28, Springer-Verlag, Berlin, 1979. |
[3] |
S. Focant and Th. Gallay, Existence and stability of propagating fronts for an autocatalytic a reaction-diffusion system, Physica D, 120 (1998), 346-368.
doi: 10.1016/S0167-2789(98)00096-7. |
[4] |
S.-C. Fu, Travelling waves of a reaction-diffusion model for the acidic nitrate-ferroin reaction, Discrete Contin. Dyn. Syst., 16 (2011), 189-196.
doi: 10.3934/dcdsb.2011.16.189. |
[5] |
S.-C. Fu, The existence of traveling wave fronts for a reaction-diffusion system modelling the acidic nitrate-ferroin reaction, Quarterly Appl. Math., to appear. |
[6] |
I. Lengyel, G. Pota and G. Bazsa, Wave profile in the acidic nitrate-ferroin reaction, J. Chem. Soc. Faraday Trans., 87 (1991), 3613-3615. |
[7] |
Y. Li and Y. Wu, Stability of travelling waves with noncritical speeds for double degenerate Fisher-type equations, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), 149-170.
doi: 10.3934/dcdsb.2008.10.149. |
[8] |
Y. Li and Y. Wu, Stability of traveling front solutions with algebraic spatial decay for some autocatalytic chemical reaction systems, SIAM J. Math. Anal., 44 (2012), 1474-1521.
doi: 10.1137/100814974. |
[9] |
J. H. Merkin and M. A. Sadiq, Reaction-diffision travelling waves in the acidic nitrate-ferroin reaction, J. Math. Chem., 17 (1995), 357-375.
doi: 10.1007/BF01165755. |
[10] |
J. D. Murray, "Mathematical Biology. I. An Introduction," Springer-Verlag, New York, 2004. |
[11] |
A. Pazy, "Semigroup of Linear Operators and Applications to Partial Differential Equations," Springer-Verlag, Berling, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[12] |
R. L. Pego and M. I. Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys., 164 (1994), 305-349. |
[13] |
G. Pota, I. Lengyel and G. Bazsa, Travelling waves in the acidic nitrate-ferroin reaction, J. Chem. Soc. Faraday Trans., 85 (1989), 3871-3877. |
[14] |
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. |
[15] |
G. Raugel and K. Kirchgässner, Stability of fronts for a KPP-system. II. The critical case, J. Differential Equations, 146 (1998), 399-456.
doi: 10.1006/jdeq.1997.3391. |
[16] |
Y. Wu, X. Xing and Q. Ye, Stability of travelling waves with algebraic decay for n-degree Fisher-type equations, Discrete Contin. Dyn. Syst., 16 (2006), 47-66.
doi: 10.3934/dcds.2006.16.47. |
[17] |
Y. Wu and X. Xing, Stability of traveling waves with critical speeds for p-degree Fisher-type equations, Discrete Contin. Dyn. Syst., 20 (2008), 1123-1139.
doi: 10.3934/dcds.2008.20.1123. |
[1] |
Sheng-Chen Fu. Travelling waves of a reaction-diffusion model for the acidic nitrate-ferroin reaction. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 189-196. doi: 10.3934/dcdsb.2011.16.189 |
[2] |
Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001 |
[3] |
Wei Wang, Wanbiao Ma. Global dynamics and travelling wave solutions for a class of non-cooperative reaction-diffusion systems with nonlocal infections. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3213-3235. doi: 10.3934/dcdsb.2018242 |
[4] |
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 |
[5] |
Anton S. Zadorin. Exact travelling solution for a reaction-diffusion system with a piecewise constant production supported by a codimension-1 subspace. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1567-1580. doi: 10.3934/cpaa.2022030 |
[6] |
Bedr'Eddine Ainseba, Mostafa Bendahmane, Yuan He. Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology. Networks and Heterogeneous Media, 2015, 10 (2) : 369-385. doi: 10.3934/nhm.2015.10.369 |
[7] |
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 |
[8] |
H. J. Hupkes, L. Morelli. Travelling corners for spatially discrete reaction-diffusion systems. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1609-1667. doi: 10.3934/cpaa.2020058 |
[9] |
Guangying Lv, Jinlong Wei, Guang-an Zou. Noise and stability in reaction-diffusion equations. Mathematical Control and Related Fields, 2022, 12 (1) : 147-168. doi: 10.3934/mcrf.2021005 |
[10] |
Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631 |
[11] |
Yansu Ji, Jianwei Shen, Xiaochen Mao. Pattern formation of Brusselator in the reaction-diffusion system. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022103 |
[12] |
Jifa Jiang, Junping Shi. Dynamics of a reaction-diffusion system of autocatalytic chemical reaction. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 245-258. doi: 10.3934/dcds.2008.21.245 |
[13] |
Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681 |
[14] |
Yuriy Golovaty, Anna Marciniak-Czochra, Mariya Ptashnyk. Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations. Communications on Pure and Applied Analysis, 2012, 11 (1) : 229-241. doi: 10.3934/cpaa.2012.11.229 |
[15] |
Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure and Applied Analysis, 2011, 10 (1) : 141-160. doi: 10.3934/cpaa.2011.10.141 |
[16] |
Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189 |
[17] |
Jiang Liu, Xiaohui Shang, Zengji Du. Traveling wave solutions of a reaction-diffusion predator-prey model. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1063-1078. doi: 10.3934/dcdss.2017057 |
[18] |
Bang-Sheng Han, Zhi-Cheng Wang. Traveling wave solutions in a nonlocal reaction-diffusion population model. Communications on Pure and Applied Analysis, 2016, 15 (3) : 1057-1076. doi: 10.3934/cpaa.2016.15.1057 |
[19] |
Vladimir V. Chepyzhov, Mark I. Vishik. Trajectory attractor for reaction-diffusion system with diffusion coefficient vanishing in time. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1493-1509. doi: 10.3934/dcds.2010.27.1493 |
[20] |
Yong Jung Kim, Wei-Ming Ni, Masaharu Taniguchi. Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3707-3718. doi: 10.3934/dcds.2013.33.3707 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]