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

被引：8

作者：

Karmakar, Debabrata ^{[1
]}

Wolansky, Gershon ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 267卷 / 12期

关键词：

Chemotaxis for multi-species; Patlak-Keller-Segel system; Minimizing movement scheme; Wasserstein distance; RADIALLY SYMMETRIC-SOLUTIONS; 2-DIMENSIONAL NAVIER-STOKES; CHEMOTAXIS MODEL; GLOBAL-SOLUTIONS; EQUATIONS; MASS; INEQUALITIES; 8-PI-PROBLEM; AGGREGATION; DIFFUSION;

D O I：

10.1016/j.jde.2019.08.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：7483 / 7520

页数：38

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