A blow-up result for attraction-repulsion system with nonlinear signal production and generalized logistic source

This paper is de & nabla;oted to studying the following chemotaxis system { u(t) = del . phi(u)del u - chi del . (u del v) + xi del . (u del pi)+lambda u(1-u(alpha)), x epsilon Omega, t > 0, 0 = Delta u - m(1)(t) + f(1) (u), m(1)(t) = 1/vertical bar Omega vertical bar integral f(1)(u), x is an element of Omega, t>0, 0 = Delta pi - m(2)(t) + f(2)(u), m(2)(t) = 1/vertical bar Omega vertical bar integral Omega f(2)(u), x epsilon Omega, t > 0, partial derivative u/partial derivative v - partial derivative v/partial derivative v - partial derivative pi/partial derivative v - 0, x epsilon partial derivative Omega, t > 0, u(x)0) = u0(x), x epsilon Omega, where Omega = B-R(0) subset of R-n(n >= 2) with R > 0, nu denotes the outward unit normal vector on partial derivative Omega, chi, xi, lambda, alpha are positive constants, and (u), f(1)(u) and f(2)(u) are suitably regular functions satisfying partial derivative(u) <= C-0(1 +u)(-m), f(1)(u) >= k(1)(u + 1)(gamma 1) and f(2)(u) <= k(2)(u+ 1)(gamma 2) for all u >= 0 with C-0, k(1), k(2), gamma 1, gamma 2 > 0 and m is an element of R. It is proved that if gamma 1 > max{alpha, gamma 2} and{ gamma 1 > 2/n(alpha + 1), if m >= 0,gamma 1+m > 2/n (alpha+1), if m < 0,then there exists a suitable initial data u0 such that the corresponding solution (u, v, pi) of the system blows up in finite time. The results of this paper extend the blow-up criteria established in Liu et al. (2021) [28]. (c) 2022 Elsevier Inc. All rights reserved.