Global Existence of Solutions to The Keller-Segal System with Initial Data of Large Mass

SHEN Ren-kun

doi:10.13371/j.cnki.chin.q.j.m.2019.04.003

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 4: 352 - 361

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.04.003

Global Existence of Solutions to The Keller-Segal System with Initial Data of Large Mass

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Department of Mathematics,College of Science,Hohai University

Online published: 2019-09-29

Supported by

Supported by the Natural Science Foundation of Jiangsu Province(BK20160856)； the National Natural Science Foundation of China(11801137)

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Abstract

In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if‖u₀‖■‖u₀‖■ and κ‖Δv₀‖Lp are less than some constant,then the problem always admits a unique global classical solution,even when the initial mass‖u₀‖L¹ is large.Moreover,the decay rates of the classical solution are also obtained.

Key words： Chemotaxis; Keller-Segel; Large mass; Global existence; Decay rate

Cite this article

SHEN Ren-kun . Global Existence of Solutions to The Keller-Segal System with Initial Data of Large Mass[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(4) : 352 -361 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.04.003

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