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arXiv · 1909.03171

Convergence to traveling waves of a singular PDE-ODE hybrid chemotaxis system in the half space

Jingyu Li·Zhian Wang
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Abstract

This paper is concerned with the asymptotic stability of the initial-boundary value problem of a singular PDE-ODE hybrid chemotaxis system in the half space $\R_+=[0, \infty)$. We show that when the non-zero flux boundary condition at $x=0$ is prescribed and the initial data are suitably chosen, the solution of the initial-boundary value problem converges, as time tend to infinity, to a shifted traveling wavefront restricted in the half space $[0,\infty)$ where the wave profile and speed are uniquely selected by the boundary flux data. The results are proved by a Cole-Hopf type transformation and weighted energy estimates along with the technique of taking {\color{black} the} anti-derivative.

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Jingyu Li, Zhian Wang. 2019-09-07. Convergence to traveling waves of a singular PDE-ODE hybrid chemotaxis system in the half space. https://arxiv.org/abs/1909.03171

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