Blow-up solutions of a chemotaxis model with nonlocal effects

In this paper, we investigate the radially symmetric solutions to the following chemotaxis system with nonlocal term ⎧ ⎨⎪⎪ ⎪⎪⎩ \l & int; /I ut = Au - V & BULL; (uVv) & mu;u 1 - u & kappa;dx , xE & OHM;, t > 0, & OHM; 0 = Av - m(t) u, xE & OHM;, t > 0, (u, v)(x, 0) = (u0(x),v0(x)), x E & OHM;, (0.1)where & OHM; := BR(0) is a ball whose center is the origin, n > 3, & mu; > 0 and f m(t) = 1 & OHM; u(x, t)dx. We show that for any m0 > 0, there exists a nonnegative |& OHM;| f initial data u0 E C1 (& OHM; over bar ) with 1 & OHM; u0dx = m0 such that the corresponding |& OHM;| solution of (0.1) blows up in finite time under the assumption 0 < & kappa; < min{2, n21.& COPY; 2023 Elsevier Ltd. All rights reserved.