We prove uniqueness in the class of integrable and bounded non- negative solutions in the energy sense to the Keller-Segel (KS) chemotaxis system. Our proof works for the fully parabolic KS model, it includes the classical parabolic-elliptic KS equation as a particular case, and it can be gen- eralized to nonlinear diffusions in the particle density equation as long as the diffusion satisfies the classical McCann displacement convexity condition. The strategy uses Quasi-Lipschitz estimates for the chemoattractant equation and the above-the-tangent characterizations of displacement convexity. As a con- sequence, the displacement convexity of the free energy functional associated to the KS system is obtained from its evolution for bounded integrable initial data.

Uniqueness for Keller-Segel-type chemotaxis models

MAININI, EDOARDO
2014

Abstract

We prove uniqueness in the class of integrable and bounded non- negative solutions in the energy sense to the Keller-Segel (KS) chemotaxis system. Our proof works for the fully parabolic KS model, it includes the classical parabolic-elliptic KS equation as a particular case, and it can be gen- eralized to nonlinear diffusions in the particle density equation as long as the diffusion satisfies the classical McCann displacement convexity condition. The strategy uses Quasi-Lipschitz estimates for the chemoattractant equation and the above-the-tangent characterizations of displacement convexity. As a con- sequence, the displacement convexity of the free energy functional associated to the KS system is obtained from its evolution for bounded integrable initial data.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/621754
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