Boundedness and finite-time blow-up in a quasilinear parabolic-elliptic chemotaxis system with logistic source and nonlinear production

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:506

Article

Tanaka, Yuya¹ 

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan

关键词: Chemotaxis;    Logistic source;    Boundedness;    Finite-time blow-up;   

DOI  :  10.1016/j.jmaa.2021.125654

来源: Elsevier

【 摘 要 】

This paper deals with the quasilinear parabolic-elliptic chemotaxis system with logistic source and nonlinear production, {u(t)=del . (D(u)del u) - del . (S(u)del v) + lambda u - mu u(Kappa), x is an element of Omega, t > 0, 0 = Delta v - M-f (t) + f (u), x is an element of Omega, t > 0, where lambda > 0, mu > 0, Kappa > 1 and M-f(t) := 1/|Omega| integral(Omega) f (u(x, t)) dx, and D, S and f are functions generalizing the prototypes D(u) = (u + 1)(m-1), S(u) = u(u + 1)(alpha-1) and f(u) = u(t) with m is an element of R, alpha > 0 and 8 > 0. In the case m = alpha = l = 1, Fuest (2021) [5] obtained conditions for Kappa such that solutions blow up in finite time. However, in the above system boundedness and finite-time blow-up of solutions have been not yet established. This paper gives boundedness and finite-time blow-up under some conditions for m, alpha, Kappa and l. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free