Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction–diffusion models. (English) Zbl 1045.45009
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.
Reviewer: J. Banaś (Rzeszów)
MSC:
| 45G10 | Other nonlinear integral equations |
| 35K57 | Reaction-diffusion equations |
| 92D25 | Population dynamics (general) |
| 45M05 | Asymptotics of solutions to integral equations |
| 45M20 | Positive solutions of integral equations |
| 35R10 | Partial functional-differential equations |
Keywords:
Nonlinear integral equations; Asymptotic speeds of spread; Traveling waves; Minimal wave speeds; Population models; Positive solutionReferences:
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