Akademik Veri Yönetim Sistemi
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, cilt.154, 2026 (SCI-Expanded, Scopus)
This paper investigates a Keller-Segel type chemotaxis model with two species, a single chemi-cal, weak nonlinear sensitivity, and Lotka-Volterra type kinetics, subject to Neumann boundary conditions in a smooth bounded domain Omega subset of R-n with n >= 2 that is, { u(t)= Delta u-chi(1)del.(u del w/w(k1))+u(a(1)-b(1)u-c(1)v),x is an element of Omega, vt= Delta v-chi(2)del.(v del w/w(k2))+v(a(2)-b(2)v-c(2)u),x is an element of Omega, 0 = Delta w-alpha w+beta u+gamma v,x is an element of Omega, where the parameters alpha, beta, gamma >0 and chi(i), a(i), b(i), c(i)> 0 for i is an element of {1,2}are positive numbers and k(1), k(2)is an element of (0,1). As is well-documented in the literature, a key step in analyzing the qualitative dynamics of chemo-taxis systems with singularities is to construct a pointwise lower bound for w since the cross-diffusive terms may blow up as we approaches zero. In contrast to previous approaches, this work departs from the classical methods and provides a new perspective. For any nonnegative initial data u(0), v(0)is an element of C-0((Omega) over bar) with u(0), v(0). not being identically zero, the following results have been established. When n = 2 problem (1) admits a unique bounded classical solution without imposing any restrictions on the parameters. When n >= 3 there exist thresholds b1 > b*1(n) and b2 >b*2(n),where the value of b*i(n) for i= 1,2 are given explicitly, such that every positive solution exists globally in the classical sense and is uniformly bounded. Alongside our theoretical analysis, we present various numerical simulations in one to four spa-tial dimensions. These simulations not only confirm our analytical results, but also offers deeper insights into the dynamics of solutions such as coexistence, extinction, and stability within the system. Interestingly, consistent with our analytical results, the numerical experiments also show that even in cases where b1 <= b*1(n)orb2 <= b*2(n), any blow-up behavior for the solutions is not observed even in 3D and 4D.