Effect of nonlinear diffusion on a lower bound for the blow-up time in a fully parabolic chemotaxis system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Nishino, Teruto¹  Yokota, Tomorni¹ 

[1] Tokyo Univ Sci, Dept Math, Tokyo, Japan

关键词: Blow-up time;    Chemotaxis system;    Nonlinear diffusion;   

DOI  :  10.1016/j.jmaa.2019.06.068

来源: Elsevier

【 摘 要 】

This paper deals with a lower bound for the blow-up time for solutions of the fully parabolic chemotaxis system {u(t) = del.[(u+alpha)(m1-1)del u - chi u(u+alpha)(m2-2)del v] in Omega x (0, T), v(t) = Delta v - v + u in Omega x (0,T) under Neumann boundary conditions and initial conditions, where Omega is a general bounded domain in R-n with smooth boundary, alpha > 0, chi > 0 , m(1), m(2) is an element of R and T > 0. Recently, Anderson-Deng [1] gave a lower bound for the blow-up time in the case that m(1) = 1 and Omega is a convex bounded domain. The purpose of this paper is to generalize the result in [1] to the case that m(1) not equal 1 and Omega is a non-convex bounded domain. The key to the proof is to make a sharp estimate by using the Gagliardo-Nirenberg inequality and an inequality for boundary integrals. As a consequence, the main result of this paper reflects the effect of nonlinear diffusion and need not assume the convexity of Omega. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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