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

2019/09/07 by Li, Jingyu, Wang, Zhian
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.03171

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, ∞). 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,∞) 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 \colorblack the anti-derivative.

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