Uniqueness of fast travelling fronts in reaction-diffusion equations with delay

Details Uniqueness of fast travelling fronts in reaction-diffusion equations with delay Uniqueness of fast travelling fronts in reaction-diffusion equations with delay

2008-04-02

arxiv.org/abs/0804.0377v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique (modulo translations). To prove the uniqueness, we introduce a small parameter 1/c and realize the Lyapunov-Schmidt reduction in a scale of Banach spaces.

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