Wavefront's stability with asymptotic phase in the delayed monostable equations

Abraham Solar; Sergei Trofimchuk

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arXiv · 2107.11938

Wavefront's stability with asymptotic phase in the delayed monostable equations

Abraham Solar·Sergei Trofimchuk

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Abstract

We extend the class of initial conditions for scalar delayed reaction-diffusion equations $u_t (t,x)=u_{xx}(t,x)+f(u(t, x), u(t-h, x))$ which evolve in solutions converging to monostable traveling waves. Our approach allows to compute, in the moving reference frame, the phase distortion $α$ of the limiting travelling wave with respect to the position of solution at the initial moment $t=0$. In general, $α\not=0$ for the Mackey-Glass type diffusive equation. Nevertheless, $α=0$ for the KPP-Fisher delayed equation: the related theorem also improves existing stability conditions for this model.

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Abraham Solar, Sergei Trofimchuk. 2021-07-26. Wavefront's stability with asymptotic phase in the delayed monostable equations. https://arxiv.org/abs/2107.11938

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