Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction--diffusion models.
The author extends a lot of results obtained earlier in the theory of asymptotic speeds of spread and monotone traveling waves to the class of nonlinear integral equations of the form \[ u(t,x)= u_0(t, x)+ \int^t_0 \int_{\mathbb R^n} F(u(t- s,x- y),s,y)\,dy\,ds,\tag{1} \] where \(F(u,s,y)= F: \mathbb R^2_+\times \mathbb R^n\to \mathbb R\) is continuous in \(u\) and Borel measurable in \((s,y)\). A lot of results concerning (1) are obtained under various additional assumptions concerning the function \(F\). The obtained results are applied to some time-delayed reaction and diffusion population models.
scientific article; zbMATH DE number 2032996
scientific article