Traveling wave fronts of reaction-diffusion systems with delay. (English) Zbl 0996.34053

Wu, Jianhong; Zou, Xingfu

J. Dyn. Differ. Equations 13, No. 3, 651-687 (2001).

Summary: The authors deal with the existence of traveling wave front solutions to reaction-diffusion systems with delay. A monotone iteration scheme is established for the corresponding wave system. If the reaction term satisfies the so-called quasi-monotonicity condition, it is shown that the iteration converges to a solution to the wave system, provided that the initial function for the iteration is chosen to be an upper solution and is from the profile set.
For systems with certain nonquasimonotone reaction terms, a convergence result is also obtained by further restricting the initial functions of the iteration and using a nonstandard ordering of the profile set.
Applications are made to the delayed Fishery-KPP equation with a nonmonotone delayed reaction term and to the delayed system of the Belousov-Zhabotinskii reaction model.

MSC:

34K10	Boundary value problems for functional-differential equations
35K57	Reaction-diffusion equations
35B20	Perturbations in context of PDEs

Keywords:

traveling wave front solutions; reaction-diffusion systems; delay; delayed Fishery-KPP equation; Belousov-Zhabotinskii reaction model