Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 18, Issue 11, Pages 3006-3013Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2013.04.025
Keywords
Nonlocal diffusion systems; Traveling wave fronts; Quiescent stage; Delay; Upper and lower solutions
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Funding
- Doctoral Research Program of Chizhou University [2011RC036]
- Scientific Research Program of Anhui Provincial Education Department [KJ2013B173]
- NNSF of China [11271379, 11071238]
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In this paper, we propose a delayed nonlocal diffusion model with a quiescent stage and study its dynamics. By using Schauder's fixed point theorem and upper-lower solution method, we establish the existence of traveling wave fronts for speed c >= c(*)(tau), where c(*)(tau) is a critical value. With the method of Carr and Chmaj (PAMS, 2004), we discuss the asymptotic behavior of traveling wave fronts and then get the nonexistence of traveling wave fronts for c < c(*)(tau). (C) 2013 Elsevier B. V. All rights reserved.
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