Traveling wave solutions for a competitive reaction-diffusion system and their asymptotics

Nonlinear Analysis: Real World Applications

Volumn 9, Issue 5, 2008, Pages 2196-2213

  Hou, Xiaojie ^a   Leung, Anthony W ^a  

^a UNIVERSITY OF CINCINNATI   (United States)

Author keywords

Asymptotics; Existence; Numerical solutions; Traveling wave; Uniqueness

Indexed keywords

ASYMPTOTIC ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; RATE CONSTANTS;

ASYMPTOTIC BEHAVIORS; ASYMPTOTIC RATES; ASYMPTOTICS; CO-EXISTENCE; EXISTENCE; LOWER SOLUTIONS; NUMERICA L RESULTS; NUMERICAL SOLUTIONS; REACTION-DIFFUSION SYSTEMS; TRAVELING WAVE; TRAVELING WAVES; TRAVELING-WAVE SOLUTIONS; UNIQUENESS; UPPER SOLUTIONS;

SOLUTIONS;

EID: 48249145301     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.07.007     Document Type: Article

References (25)

1. Ahmad S., and Lazer A. An elementary approach to traveling front solutions to a system of N competition-diffusion equations. Nonlinear Anal. 16 10 (1991) 893-901
2. Berestycki H., Nicolaenko B., and Scheurer B. Travelling wave solutions to combustion models and their singular limits. SIAM J. Math. 16 6 (1985) 1207-1242
3. Berestycki H., and Nirenberg L. Travelling fronts in cylinders. Ann. Inst. H. Poincare Anal. Non Lineaire 9 5 (1992) 497-572
4. Conley C., and Gardner R. An application of the generalized Morse index to traveling wave solutions of a competitive reaction diffusion model. Indiana Univ. Math. J. 33 (1984) 319-345
5. Coppel W. Stability and Asymptotic Behavior of Differential Equations, Heath Mathematical Monographs (1965), D.C. Heath and Company, Boston
6. 4. Trans. Am. Math. Soc. 286 2 (1984) 557-594
7. Gardner R. Existence of traveling wave solutions of competing models, A degree theoretic approach. J. Differential Equations 44 (1982) 343-364
8. Hallam T., and Lika K. Traveling wave solutions of a nonlinear reaction-advection equation. J. Math. Biol. 38 4 (1999) 346-358
9. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer, NY, 1981.
10. Hess P. Periodic-Parabolic Boundary Value Problems and Positivity (1991), Pitman, R.N.M., Longman, Harlow
11. Hou X., and Li Y. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete Continuous Dynamical Syst. 15 2 (2006) 681-701
12. Huang J., and Zou X. traveling wavefronts in diffusive and cooperative Lotka-Voltera system with delays. J. Math. Anal. Appl. 271 (2002) 455-466
13. Kirchgassner K. On the nonlinear dynamics of travelling fronts. J. Differential Equations 96 (1992) 256-278
14. Leung A. Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering (1989), MIA, Kuwer, Boston
15. Li B., Weinberger H., and Lewis M. Spreading speeds as slowest wave speeds for cooperative systems. Math. Biosci. 196 (2005) 82-98
16. Lui R. Biological growth and spread modeled by systems of recursions. I. Mathematical Theory, Math. Biosci. 93 (1989) 269-295
17. Pao C. Nonlinear Parabolic and Elliptic Equations (1992), Plenum Press, NY
18. Sattinger D.H. On the stability of waves of nonlinear parabolic systems. Adv. Math. 22 (1976) 312-355
19. Smith H. Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems (1995), AMS Providence, RI
20. Smoller J. Shock Waves and Reaction-Diffusion Equations (1982), Springer, NY
21. Tang M., and Fife P. Propagating fronts for competing species with diffusion. Arch. Ration. Mech. Anal. 73 (1978) 69-77
22. Van Vuuren J. The existence of traveling plane waves in a general class of competition-diffusive systems. IMA J. Appl. Math. 55 (1995) 135-148
23. I. Volpert, V. Volpert, V. Volpert, Traveling Wave Solutions of Parabolic Systems, Translations of Mathematics Monograph, vol. 140, American Mathematical Society, Providence, RI, 1994.
24. Wu J., and Zou X. Traveling wave fronts of reaction-diffusion systems with delay. J. Dyn. Differential Equations 13 3 (2001)
25. Xin J. Front propagation in heteogeneous media. SIAM Rev. 42 2 (2000) 161-230