The paper is devoted to the study of a time-delayed reaction-
diffusion equation of age-structured single species population. Linear stability
for this model was first presented by Gourley [4], when the time delay is small.
Here, we extend the previous result to the nonlinear stability by using the
technical weighted-energy method, when the initial perturbation around the
wavefront decays to zero exponentially as x→-∞, but the initial perturbation
can be arbitrarily large on other locations. The exponential convergent rate
(in time) of the solution is obtained. Numerical simulations are carried out to
confirm the theoretical results, and the traveling wavefronts with a large delay
term in the model are reported.
Citation: Guangrui Li, Ming Mei, Yau Shu Wong. Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model[J]. Mathematical Biosciences and Engineering, 2008, 5(1): 85-100. doi: 10.3934/mbe.2008.5.85
Abstract
The paper is devoted to the study of a time-delayed reaction-
diffusion equation of age-structured single species population. Linear stability
for this model was first presented by Gourley [4], when the time delay is small.
Here, we extend the previous result to the nonlinear stability by using the
technical weighted-energy method, when the initial perturbation around the
wavefront decays to zero exponentially as x→-∞, but the initial perturbation
can be arbitrarily large on other locations. The exponential convergent rate
(in time) of the solution is obtained. Numerical simulations are carried out to
confirm the theoretical results, and the traveling wavefronts with a large delay
term in the model are reported.