Asymptotic decay for the solutions of the parabolic–parabolic Keller–Segel chemotaxis system in critical spaces (original) (raw)

Mathematical and Computer Modelling, 2008

Abstract

We consider the classical parabolic–parabolic Keller–Segel system describing chemotaxis, i.e., when both the evolution of the biological population and the chemoattractant concentration are described by a parabolic equation. We prove that when the equation is set in the whole space Rd and dimension d≥3 the critical spaces for the initial bacteria density and the chemical gradient are respectively La(Rd), a>d/2,

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