No abstract

In this paper, we provide a general approach to study the asymptotic behavior of traveling wave solutions for a three-component system with nonlocal dispersal. Then as an important application, we establish a new type of entire solutions which behave as two traveling wave solutions coming from both sides of x-axis for a three-species Lotka-Volterra competition system.2010 Mathematics Subject Classification. Primary: 35K57, 37K65; Secondary: 92D30.

No abstract

This paper is concerned with entire solutions for a two-dimensional periodic lattice dynamical system with nonlocal dispersal. In the bistable case, by applying comparison principle and constructing appropriate upper-and lowersolutions, two different types of entire solutions are constructed. The first type behaves like a monostable front merges with a bistable front and one chases another from the same side; while the other type can be represented by two monostable fronts merge and converge to a single bistable front. In the monostable case, we first establish the existence and properties of spatially periodic solutions which connect two steady states. Then new types of entire solutions are constructed by mixing a heteroclinic orbit of the spatially averaged ordinary differential equations with traveling wave fronts with different speeds. Further, for a class of special heterogeneous reaction function, we establish the uniqueness and continuous dependence of the entire solution on parameters, such as wave speeds and shifted variables. k1 k2 J(k 1 , k 2)u i−k1,j−k2 (t) − u i,j (t) is the nonlocal dispersal and represents transportation due to long range dispersion mechanism. The kernel function J : Z × Z → [0, ∞), is a probability function formulating the dispersal of individuals and satisfies (J): J(•, •) ≥ 0 is even, k1 k2 J(k 1 , k 2) = 1, J(k 1 , k 2) = 0 if |k 1 | > k 0 or |k 2 | > k 0 , where k 0 is a positive constant. The reaction term f i,j (•), i, j ∈ Z satisfies