文献详情
On Global Solutions and Blow-Up for a Short-Ranged Chemical Signaling Loop
文献类型：期刊
通讯作者：Lin, K (reprint author), Southwestern Univ Finance & Econ, Coll Econ Math, Chengdu 611130, Sichuan, Peoples R China.
期刊名称：JOURNAL OF NONLINEAR SCIENCE影响因子和分区
年：2019
卷：29
期：2
页码：551-591
ISSN：0938-8974
关键词：Loop chemotaxis; Simultaneous boundedness; Simultaneous blow-up; Critical mass phenomenon
所属部门：数学科学研究院
摘要：This paper aims at providing a substantial step toward the global boundedness and blow-up of solutions to a two-species and two-stimuli chemotaxis model, in which the process of the species results in a short-ranged chemical signaling loop. More precisely, we consider the following Neumann initial-boundary value problem {u(t) = Delta u - chi(1)del . (u del v), x is an element of Omega, t > 0, 0 = Delta v - mu(2) + w, x is an element of Omega, t > 0, w(t) = Delta w - chi(2)del center dot ...More
This paper aims at providing a substantial step toward the global boundedness and blow-up of solutions to a two-species and two-stimuli chemotaxis model, in which the process of the species results in a short-ranged chemical signaling loop. More precisely, we consider the following Neumann initial-boundary value problem {u(t) = Delta u - chi(1)del . (u del v), x is an element of Omega, t > 0, 0 = Delta v - mu(2) + w, x is an element of Omega, t > 0, w(t) = Delta w - chi(2)del center dot (w del z) - chi(3)del . (w del v), x is an element of Omega, t > 0, 0 = Delta z - mu(1) + u, x is an element of Omega, t > 0 in the unit disk Omega:=B-1(0) subset of R-2 with chemotactic sensitivities chi(1) > 0, chi(2) > 0 and chi(3) >= 0 and radially symmetric nonnegative initial data u(0) and w(0), where mu(1) and mu(2) are given, respectively, by mu(1) := m1 and 2:=m2 with m1=u0, m2=w0.Explicit conditions on i,i, u0 and w0 are given for the simultaneous global boundedness and simultaneous finite-time blow-up of classical solutions. Specifically, when the effect of 3>0 is strong enough in the sense that the dynamical properties of the above system behave like one single-species Keller-Segel chemotaxis system, it is shown that if only the total mass m2<41 and m2<43, the solutions are globally bounded, while blow-up may occur provided that m2>41 and m2>83. Moreover, in view of the chemotactic signaling loop, one can find a critical mass phenomenon:if 2m1+m232<82, the problem possesses only globally bounded solutions, whereasif 8m11+8m22<2m1m2+m22 32 and u0|x|2 and w0|x|2 are sufficiently small, the corresponding solution blows up in finite time in the sense that lim sup (parallel to u(., t)parallel to(L infinity(Omega)) + parallel to w(., t)parallel to(L infinity(Omega))) -> infinity with some finite time T>0. The simultaneous blow-up phenomenon for two species is also given in this paper.This, in particular, shows, when chi(3)=0, that smallness of mass of each species implies global solvability, whereas largeness of masses induces blow-up to occur. ...Hide

DOI：10.1007/s00332-018-9494-6
百度学术：On Global Solutions and Blow-Up for a Short-Ranged Chemical Signaling Loop
语言：外文
被引频次：1
基金：Fundamental Research Funds for the Central UniversitiesFundamental Research Funds for the Central Universities [JBK1801059]; NSFCNational Natural Science Foundation of China [11801461, 11601516]; Research Funds of Renmin University of China [2018030199]
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