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Travelling wavefronts in the diffusive single species model with Allee effect and distributed delay. (English) Zbl 1041.92027

Summary: We consider a diffusive single species model with Allee effect and distributed delay time. Special attention is paid to the existence of travelling wavefront solutions. First, we show that such fronts exist when the convolution kernel assumes a strong generic delay kernel and the delay is sufficiently small. Then, in the non-local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times, we show that such fronts still exist for weak generic delay kernels and small delay. The approach used in this paper is the geometric singular perturbation theory.

MSC:

92D25 Population dynamics (general)
35B25 Singular perturbations in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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