Article

Global Stability of Monostable Traveling Waves For Nonlocal Time-Delayed Reaction-Diffusion Equations.

SIAM Journal on Mathematical Analysis (Impact Factor: 1.4). 01/2010; 42(6):2762-2790. DOI: 10.1137/090776342
Source: DBLP

ABSTRACT For spatial dynamics of a single-species population with age-structure and spatial diffusion such as the Australian blowflies population distribution, a class of time-delayed reaction-diffusion equations with nonlocal nonlinearity abounds in the literature. For such a class of (nonlocal time-delayed reaction-diffusion) equations, the authors prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near the negative infinity regardless of the magnitude of time delay. Their approach is based on the combination of the weighted energy method and the Green function technique. The study improves and develops the existing stability results for local and nonlocal reaction-diffusion equations with delays. An erratum to this study to fix the gap in the proof of Lemma 3.8 is provided online at http://www.math.mcgill.ca/~mei/Erratum.pdf.

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