Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity

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Abstract

This paper is concerned with the spreading speeds and traveling wave solutions of a nonlocal dispersal equation with degenerate monostable nonlinearity. We first prove that the traveling wave solution φ(ξ) with critical minimal speed c=c * decays exponentially as ξ→-∞, while other traveling wave solutions φ(ξ) with c>c * do not decay exponentially as ξ→-∞. Then the monotonicity and uniqueness (up to translation) of traveling wave solution with critical minimal speed is established. Finally, we prove that the critical minimal wave speed c * coincides with the asymptotic speed of spread. © 2012 Elsevier Inc.

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Zhang, G. B., Li, W. T., & Wang, Z. C. (2012). Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity. Journal of Differential Equations, 252(9), 5096–5124. https://doi.org/10.1016/j.jde.2012.01.014

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