The pointwise estimates of solutions to the Cauchy problem of a chemotaxis model

Abstract

This paper deals with an attraction-repulsion chemotaxis model (ARC) in multi-dimensions. By Duhamel’s principle, the implicit expression of the solution to (ARC) is given. With the method of Green’s function, the authors obtain the pointwise estimates of solutions to the Cauchy problem (ARC) for small initial data, which yield the W ^s,p (1 ≤ p ≤ ∞) decay properties of solutions.

Keywords

Chemotaxis model / Pointwise estimates / Green’s function / Decay rates

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