Abstract
This paper is concerned with the traveling wave solutions of delayed reaction–diffusion systems. By using Schauder’s fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka–Volterra competition systems with distributed delays are established. The existence of nonmonotone traveling wave solutions of diffusive Lotka–Volterra competition systems is also discussed. In particular, it is proved that if there exists instantaneous self-limitation effect, then the large delays appearing in the intra-specific competitive terms may not affect the existence and asymptotic behavior of traveling wave solutions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 583-605 |
| Number of pages | 23 |
| Journal | Journal of Dynamics and Differential Equations |
| Volume | 26 |
| Issue number | 3 |
| DOIs | |
| State | Published - Nov 4 2014 |
Fingerprint
Keywords
- Contracting rectangle
- Generalized upper and lower solutions
- Invariant region
- Nonmonotone traveling wave solutions
ASJC Scopus subject areas
- Analysis
Cite this
Traveling Wave Solutions for Delayed Reaction–Diffusion Systems and Applications to Diffusive Lotka–Volterra Competition Models with Distributed Delays. / Lin, Guo; Ruan, Shigui.
In: Journal of Dynamics and Differential Equations, Vol. 26, No. 3, 04.11.2014, p. 583-605.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Traveling Wave Solutions for Delayed Reaction–Diffusion Systems and Applications to Diffusive Lotka–Volterra Competition Models with Distributed Delays
AU - Lin, Guo
AU - Ruan, Shigui
PY - 2014/11/4
Y1 - 2014/11/4
N2 - This paper is concerned with the traveling wave solutions of delayed reaction–diffusion systems. By using Schauder’s fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka–Volterra competition systems with distributed delays are established. The existence of nonmonotone traveling wave solutions of diffusive Lotka–Volterra competition systems is also discussed. In particular, it is proved that if there exists instantaneous self-limitation effect, then the large delays appearing in the intra-specific competitive terms may not affect the existence and asymptotic behavior of traveling wave solutions.
AB - This paper is concerned with the traveling wave solutions of delayed reaction–diffusion systems. By using Schauder’s fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka–Volterra competition systems with distributed delays are established. The existence of nonmonotone traveling wave solutions of diffusive Lotka–Volterra competition systems is also discussed. In particular, it is proved that if there exists instantaneous self-limitation effect, then the large delays appearing in the intra-specific competitive terms may not affect the existence and asymptotic behavior of traveling wave solutions.
KW - Contracting rectangle
KW - Generalized upper and lower solutions
KW - Invariant region
KW - Nonmonotone traveling wave solutions
UR - http://www.scopus.com/inward/record.url?scp=84912049267&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84912049267&partnerID=8YFLogxK
U2 - 10.1007/s10884-014-9355-4
DO - 10.1007/s10884-014-9355-4
M3 - Article
AN - SCOPUS:84912049267
VL - 26
SP - 583
EP - 605
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
SN - 1040-7294
IS - 3
ER -