TY - JOUR
T1 - On travelling wavefronts of Nicholson's blowflies equation with diffusion
AU - Lin, Chi Kun
AU - Mei, Ming
N1 - Funding Information:
The authors express their sincere thanks to the referee for a valuable suggestion that led them to further study the stability of the wavefronts with a general birthrate function. The authors also thank Dr Guangrui Li for the help in numerical computations. The work was partly done in 2005 when M.M. visited the National Center for Theoretical Sciences (South), Taiwan. He expresses his sincere thanks for their great hospitality. The research of C.-K.L. was supported in part by the National Science Council of Taiwan under Grant no. 95-2115-M-009-MY3, and the research of M.M. was supported in part by the Natural Sciences and Engineering Research Council of Canada under NSERC Grant no. RGPIN 354724-08.
PY - 2010/2
Y1 - 2010/2
N2 - This paper is devoted to the study of Nicholson's blowflies equation with diffusion: a kind of time-delayed reaction diffusion. For any travelling wavefront with speed c >c* (c* is the minimum wave speed), we prove that the wavefront is time-asymptotically stable when the delay-time is sufficiently small, and the initial perturbation around the wavefront decays to zero exponentially in space as x → -∞, but it can be large in other locations. The result develops and improves the previous wave stability obtained by Mei et al. in 2004. The new approach developed in this paper is the comparison principle combined with the technical weighted-energy method. Numerical simulations are also carried out to confirm our theoretical results.
AB - This paper is devoted to the study of Nicholson's blowflies equation with diffusion: a kind of time-delayed reaction diffusion. For any travelling wavefront with speed c >c* (c* is the minimum wave speed), we prove that the wavefront is time-asymptotically stable when the delay-time is sufficiently small, and the initial perturbation around the wavefront decays to zero exponentially in space as x → -∞, but it can be large in other locations. The result develops and improves the previous wave stability obtained by Mei et al. in 2004. The new approach developed in this paper is the comparison principle combined with the technical weighted-energy method. Numerical simulations are also carried out to confirm our theoretical results.
UR - https://www.scopus.com/pages/publications/77949668907
U2 - 10.1017/S0308210508000784
DO - 10.1017/S0308210508000784
M3 - Article
AN - SCOPUS:77949668907
SN - 0308-2105
VL - 140
SP - 135
EP - 152
JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
IS - 1
ER -