Global boundedness and blow-up in a repulsive chemotaxis-consumption system in higher dimensions

Abstract

This paper investigates the repulsive chemotaxis-consumption model partial derivative(t)u = del . (D(u) del u) + V . (u del v), 0 = Delta v-uv, in an n-dimensional ball, n >= 3, where the diffusion coefficient D is an appropriate extension of the function 0 <= xi bar right arrow (1 + xi)(m-1) for m > 0. Under the boundary conditions nu . (D(u) del u + u del v) = 0 and v = M > 0, we demonstrate that for m > 1, or m = 1 and 0 < M < 2/(n - 2), the system admits globally bounded classical solutions for any choice of sufficiently smooth radial initial data. This result is further extended to the case 0 < m < 1 when M is chosen to be sufficiently small, depending on the initial conditions. In contrast, it is shown that for 0 < m < 2/n, the system exhibits blow-up behavior for sufficiently large M. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.