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arXiv · 1902.10736

On Patlak-Keller-Segel system for several populations: a gradient flow approach

Debabrata Karmakar·Gershon Wolansky
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Abstract

We study the global in time existence of solutions to the parabolic-elliptic Patlak-Keller-Segel system of multi-species populations. We prove that if the initial mass satisfies an appropriate notion of sub-criticality, then the system has a solution defined for all time. We explore the gradient flow structure in the Wasserstein space to study the question of existence. Moreover, we show that the obtained solution satisfies energy dissipation inequality.

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Debabrata Karmakar, Gershon Wolansky. 2019-02-27. On Patlak-Keller-Segel system for several populations: a gradient flow approach. https://arxiv.org/abs/1902.10736

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