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Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays. (English) Zbl 1100.35050

The existence of travelling wave solutions to delayed systems of reaction-diffusion type, which is studied by the authors of the article under review, is equivalent to the existence of solutions to some second order system of functional differential equations (FDEs). By employing some kinds of quasi-monotonicity, the authors prove the existence of solutions to the FDE system by contructing the solutions through an iteration method whose convergence is ensured by the quasi-monotonicity used there. The authors show also how their theory can be applied to treat a lot of concrete delayed systems of reaction-diffusion type.

MSC:

35K57 Reaction-diffusion equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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