Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model - Guangrui Li; Ming Mei; Yau Shu Wong (Mathematical Biosciences and Engineering)
The paper is devoted to the study of a time-delayed reaction-diffusion equation of age-structured single species population. Linear stabilityfor 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 thetechnical weighted-energy method, when the initial perturbation around thewavefront decays to zero exponentially as x→-∞, but the initial perturbationcan be arbitrarily large on other locations. The exponential convergent rate(in time) of the solution is obtained. Numerical simulations are carried out toconfirm the theoretical results, and the traveling wavefronts with a large delayterm in the model are reported.