Finite-time blow-up and global boundedness for chemotaxis system with strong logistic dampening

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Tu, Xinyu¹  Qiu, Shuyan² 

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] Chongqing Univ, Dept Math & Stat, Chongqing 401331, Peoples R China

关键词: Chemotaxis system;    Logistic source;    Radially symmetric solutions;    Finite-time blow-up;   

DOI  :  10.1016/j.jmaa.2020.123876

来源: Elsevier

【 摘 要 】

In the present study, we consider the chemotaxis system with logistic-type superlinear degradation {partial derivative(t)u(1)= tau(1)Delta u(1) - chi(1)del . (u(1)del(v)) + lambda(1)u(1) - mu(1)u(1)(k1), x is an element of Omega, t > 0, partial derivative(tau)u(2) = tau(2)Delta u(2) - chi(2)del . (u(2)del v) + lambda(2)u(2) - mu(2)u(2)(k2), x is an element of Omega, t > 0, 0 = Delta v - gamma v + alpha(1)u(1) + alpha(2)u(2), x is an element of Omega, t > 0, under the homogeneous Neumann boundary condition, where gamma > 0, tau(i) > 0, chi(i) > 0, lambda(i) is an element of R, mu(i) > 0, alpha(i) > 0 (i = 1, 2). Consider an arbitrary ball Omega = B-R(0) subset of R-n, n >= 3, R > 0, when k(i) > 1(i = 1,2), it is shown that for any parameter (k) over cap = max{k(1), k(2)} satisfies (k) over cap < {7/6 if n is an element of {3,4}, 1 + 1/2(n-1) if n >= 5, there exist nonnegative radially symmetric initial data under suitable conditions such that the corresponding solutions blow up in finite time in the sense that lim sup(t NE arrow Tmax) (parallel to u(1)(.t)parallel to(L infinity(Omega)) + parallel to u(2)(.,t)parallel to(L infinity(Omega))) = infinity for some 0 < T-max < infinity. Furthermore, for any smooth bounded domain Omega C R-n(n >= 1), when k(i )>= 2(i = 1, 2), we prove that the system admits a unique global bounded solution. (C) 2020 Elsevier Inc. All rights reserved.

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