高维空间信号依赖型Keller-Segel系统的有限时刻爆破  

Finite-Time Blow-Up in the Higher-Dimensional Keller-Segel System With Signal-Dependent Motility

作　　者：卢疏颖 李燕 LU Shuying;LI Yan(School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]南京邮电大学理学院,江苏南京210023

出　　处：《中北大学学报（自然科学版）》2023年第2期109-115,共7页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金青年基金(11701290);江苏省自然科学基金青年基金(BK20170896);江苏省自然科学研究面上项目(21KJB110031,17KJB110012)。

摘　　要：本文研究了具有密度抑制效应的抛物-抛物型Keller-Segel系统的Neumann初边值问题:{u_(t)=Δ(γ(v)u),x∈Ω,t>0,v_(t)=Δv-v+u,x∈Ω,t>0的有限时刻爆破,其中,Ω为R^(n)(n≥3)中的光滑有界球形区域,γ(v)为扩散强度。本文考虑了指数型的扩散速率γ(v)=e-χv,其中χ为常数。证明了对于任意的初始聚集量∫_(Ω)u_(0)=m(m>0),存在满足一定低能条件的径向对称的初值(u_(0),v_(0))∈C^(0)(×W^(1,∞)(Ω)),使得系统的解会在有限时刻发生爆破。We studied the Neumann initial-boundary value problem for the fully parabolic Keller-Segel system with density-inhibiting effect {u_(t)=Δ(γ(v)u),x∈Ω,t>0,v_(t)=Δv-v+u,x∈Ω,t>0 whereΩis the smooth bounded spherical region in R n with n≥3,functionγ(v)describes the strength of diffusion.In this paper,we choose the exponential diffusion rateγ(v)=e^(-χv),whereχis a constant.It is proved that for any prescribed m>0 there exist radially symmetric positive initial data(u_(0),v_(0))∈C^(0)(Ω×W^(1,∞)(Ω))with∫_(Ω)u^(0)=m(m>0)such that the corresponding solution blows up in finite time.

关 键 词：Keller-Segel模型 信号依赖型扩散 径向对称解 有限时刻爆破 LYAPUNOV泛函 

分 类 号：O175.29[理学—数学]