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Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model. (English) Zbl 1148.35038
Summary: 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 S. A. Gourley [Q. J. Mech. Appl. Math. 58, No. 2, 257–268 (2005; Zbl 1069.92018)], 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 $$x\to-\infty$$, 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.

##### MSC:
 35K57 Reaction-diffusion equations 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general) 35R10 Functional partial differential equations
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