Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system
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 \[ \begin{cases}\frac {\partial u}{\partial t}= d\Delta u+d\int^T_0\int_\mathbb{R} F(s,y)u(t-s,x-y)dy\,ds-\beta u^2(t,x)\\ \frac {\partial v}{\partial t}=D\Delta v-\gamma v+ \alpha u-\alpha\int^T_0\int_\mathbb{R} F (s,y)u(t-s,x-y)dy\,ds,\end{cases} \tag{1} \] where \(\tau\in(0,\infty],d,D,\alpha,\beta, \gamma\) are positive and \(F:\mathbb{R}^2\to\mathbb{R}\) satisfies natural assumptions.
scientific article; zbMATH DE number 5365150
scientific article