Traveling waves and their stability in a coupled reaction diffusion system
Pages: 141  160,
Volume 10,
Issue 1,
January
2011
doi:10.3934/cpaa.2011.10.141 Abstract
References
Full text (459.6K)
Related Articles
Xiaojie Hou  Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403, United States (email)
Wei Feng  Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403, United States (email)
1 
S. Ai, SN. Chow and Y. Yi, Traveling wave solutions in a tissue interaction model for skin pattern formation, Journal of Dynamics and Differential Equations, 15 (2003), 517534. 

2 
J. C. Alexander, R. A. Gardner and C. K. R. T. Jones, A topological invariant arising in the stability analysis of traveling waves, J. Reine Angew Math., 410 (1990), 167212. 

3 
M. Arias, J. Campos and C. Marcelli, Fastness and continuous dependence in front propagation in FisherKPP equations, Discrete and Continuous Dynamical SystemsB, 11 (2009), 1130. 

4 
P. W. Bates and F. Chen, Spectral analysis and multidimensional stability of traveling waves for nonlocal AllenCahn equation, J. Math. Anal. Appl., 273 (2002), 4557. 

5 
A. Boumenir and V. Nguyen, Perron theorem in monotone iteration method for traveling waves in delayed reactiondiffusion equations, Journal of Differential Equations, 244 (2008), 15511570. 

6 
E. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," McGrawHill, 1955. 

7 
N. Fei and J. Carr, Existence of travelling waves with their minimal speed for a diffusing LotkaVolterra system, Nonlinear Analysis: Real World Applications, 4 (2003), 503524. 

8 
Th. Gallay, G. Schneider and H. Uecker, Stable transport of information near essentially unstable localized structures, Discrete and Continuous Dynamical SystemsB, 4 (2004), 349390. 

9 
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, 840, SpringerVerlag, 1981. 

10 
Y. Hosono, Travelling waves for a diffusive LotkaVolterra competition model I: Singular Perturbations, Discrete Continuous Dynamical SystemsB, 3 (2003), 7995. 

11 
X. Hou, W. Feng and X. Lu, A mathematical analysis of a pubilc goods games model, Nonlinear Analysis: Real World Applications, 10 (2009), 22072224. 

12 
X. Hou and Y. Li, Local stability of traveling wave solutions of nonlinear reaction diffusion equations, Discrete and Continuous Dynamical SystemsA, 15 (2006), 681701. 

13 
X. Hou, Y. Li and K. R. Meyer, Traveling wave solutions for a reaction diffusion equation with double degenerate nonlinearities, Discrete and Continuous Dynamical SystemsA, 26 (2010), 265290. 

14 
W. Huang, Uniqueness of traveling wave solutions for a biological reactiondiffusion equation, J. Math. Anal. Appl., 316 (2006), 4259. 

15 
J. I Kanel, On the wave front of a competitiondiffusion system in popalation dynamics, Nonlinear Analysis: Theory, Methods & Applications, 65 (2006), 301320. 

16 
J. I Kanel and Li Zhou, Existence of wave front solutions and estimates of wave speed for a competitiondiffusion system, Nonlinear Analysis: Theory, Methods & Applications, 27 (1996), 579587. 

17 
Y. Kanon, Note on propagation speed of travelling waves for a weakly coupled parabolic system, Nonlinear Analysis: Theory, Methods & Applications, 44 (2001), 239246. 

18 
Y. Kanon, Fisher wave fronts for the lotkavolterra competition model with diffusion, Nonlinear Analysis: Theory, methods & Applications, 28 (1997), 145164. 

19 
T. Kapitula, On the stability of Traveling waves in weighted $L^\infty$ spaces, Journal of Differential Equations, 112 (1994), 179215. 

20 
A. Kolmogorov, A. Petrovskii and N. Piskunov, A study of the equation of diffusion with increase in the quantity of matter, Bjul. Moskovskovo Gov. Iniv., 17 (1937), 172. 

21 
J. Li, Bifurcations of travelling wave solutions for two generalized Boussinesq systems, Science in China Series A, 51 (2008), 15771592. 

22 
X. Liao, X. Tang and S. Zhou, Existence of traveling wavefronts in a cooperative systems with discrete delays, Applied Mathematics and Computation, 215 (2009), 18061812. 

23 
S. W. Ma, Traveling waves for nonlocal delayed diffusion equations via auxiliary equations, Journal of Differential Equations, 237 (2007), 259277. 

24 
P. Maini, L. Malaguti, C. Marcelli and S. Matucci, Diffusionaggregation processes with monostable reaction terms, Discrete and Continuous Dynamical SystemsB, 6 (2006), 11751189. 

25 
Y. Qi, Travelling fronts of reaction diffusion systems modeling autocatalysis, Discrete and Continuous Dynamical Systems, suppl. Volume (2009), 622629. 

26 
B. Sandstede, Stability of traveling waves, in "Handbook of Dynamical Systems II" (B Fiedler, ed.). NorthHolland (2002), 9831055. 

27 
D. Sattinger, On the stability of traveling waves of nonlinear parabolic systems, Advances in Mathematics, 22 (1976), 312355. 

28 
M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion, Arch. Rat. Mech. Anal., 73 (1980), 6977. 

29 
A. Volpert, V. Volpert and V. Volpert, "Traveling Wave Solutions of Parabolic Systems," Transl. Math. Monograhs 140, Amer. Math. Soc., Providence, RI., 1994. 

30 
J. Y. Wakano, A mathematical analysis on public goods games in the continuous space, Math. Biosciences, 201 (2006), 7289. 

31 
ZC. Wang, WT. Li and S. Ruan, Existence and Stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay, Journal of Differential Equations, 238 (2007), 153200. 

32 
J. Wu and X. Zou, Traveling wave fronts of reactiondiffusion systems with delay, Journal of Dynamics and Differential Equations, 13 (2001), 51687, and Erratum to traveling wave fronts of reactiondiffusion systems with delays, Journal of Dynamics and Differential Equations, 20 (2008), 531533. 

33 
Y. Wu and Y. Li, Stability of travelling waves with noncritical speeds for double degenerate Fishertype equations, Discrete Continuous Dynamical SystemsB, 10 (2008), 149170. 

34 
D. Xu and X.Q. Zhao, Bistable waves in an epidemic model, Journal of Dynamics and Differential Equations, 16 (2004), 679707, and Erratum, Journal of Dynamics and Differential Equations, 17 (2005), 219247. 

35 
Y.Wu, X. Xing and Q. Ye, Stability of travelling waves with algebraic decay for $n$degree Fishertype equations, Discrete and Continuous Dynamical SystemsB, 16 (2006), 4766. 

36 
XQ Zhao and W. Wang, Fisher waves in an epidemic model, Discrete and Continuous Dynamical SystemsB, 4 (2004), 11171128. 

Go to top
