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Search: MSC category 35K57 ( Reaction-diffusion equations )

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1. CMB Online first

Liu, Li; Weng, Peixuan
Globally asymptotic stability of a delayed integro-differential equation with nonlocal diffusion
We study a population model with nonlocal diffusion, which is a delayed integro-differential equation with double nonlinearity and two integrable kernels. By comparison method and analytical technique, we obtain globally asymptotic stability of the zero solution and the positive equilibrium. The results obtained reveal that the globally asymptotic stability only depends on the property of nonlinearity. As application, an example for a population model with age structure is discussed at the end of the article.

Keywords:integro-differential equation, nonlocal diffusion, equilibrium, globally asymptotic stability, population model with age structure
Categories:45J05, 35K57, 92D25

2. CMB 2011 (vol 56 pp. 659)

Yu, Zhi-Xian; Mei, Ming
Asymptotics and Uniqueness of Travelling Waves for Non-Monotone Delayed Systems on 2D Lattices
We establish asymptotics and uniqueness (up to translation) of travelling waves for delayed 2D lattice equations with non-monotone birth functions. First, with the help of Ikehara's Theorem, the a priori asymptotic behavior of travelling wave is exactly derived. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. These results complement earlier results in the literature.

Keywords:2D lattice systems, traveling waves, asymptotic behavior, uniqueness, nonmonotone nonlinearity
Category:35K57

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