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Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system. (English) Zbl 1180.35536
The goal of this paper is to study the asymptotic speed of spread, the existence and nonexistence of travelling wave for the following nonlocal and time-delayed reaction-diffusion system $$\cases\frac {\partial u}{\partial t}= d\Delta u+d\int^T_0\int_\bbfR F(s,y)u(t-s,x-y)dy\,ds-\beta u^2(t,x)\\ \frac {\partial v}{\partial t}=D\Delta v-\gamma v+ \alpha u-\alpha\int^T_0\int_\bbfR F (s,y)u(t-s,x-y)dy\,ds,\endcases \tag1$$ where $\tau\in(0,\infty],d,D,\alpha,\beta, \gamma$ are positive and $F:\bbfR^2\to\bbfR$ satisfies natural assumptions.

35R10Partial functional-differential equations
35K57Reaction-diffusion equations
35B40Asymptotic behavior of solutions of PDE
92D25Population dynamics (general)
Full Text: DOI
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