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- Title
STABILITY OF TRAVELING WAVES FOR NONLOCAL TIME-DELAYED REACTION-DIFFUSION EQUATIONS.
- Authors
Jiang, Yicheng; Zhang, Kaijun
- Abstract
This paper is concerned with the stability of noncritical/critical traveling waves for nonlocal time-delayed reaction-diffusion equation. When the birth rate function is non-monotone, the solution of the delayed equation is proved to converge time-exponentially to some (monotone or non-monotone) traveling wave profile with wave speed c > c*, where c* > 0 is the minimum wave speed, when the initial data is a small perturbation around the wave. However, for the critical traveling waves (c = c*), the time-asymptotical stability is only obtained, and the decay rate is not gotten due to some technical restrictions. The proof approach is based on the combination of the anti-weighted method and the nonlinear Halanay inequality but with some new development.
- Subjects
STABILITY theory; TIME delay systems; TRAVELING waves (Physics); REACTION-diffusion equations; MATHEMATICAL functions; MATHEMATICAL inequalities
- Publication
Kinetic & Related Models, 2018, Vol 11, Issue 5, p1235
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2018048