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--> -infinity, 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.
Highlights
The population of a single species with age-structure is usually described as a time delayed reaction-diffusion equation
By using the comparison principle together with the weighted energy method, we prove the following nonlinear stability of traveling wavefronts even when the initial perturbations are not small
We prove the stability of the traveling wavefronts by the weighted energy method
Summary
Time-delayed reaction-diffusion equation, traveling wavefronts, nonlinear stability, exponential decay rate. To prove the stability of traveling waves with large initial perturbations for the Nicholson’s blowflies equation.
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