Akademik Veri Yönetim Sistemi
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, cilt.86, 2025 (SCI-Expanded)
This paper concerns with the following parabolic-elliptic chemotaxis-growth system with weak singular sensitivity {u(t )= Delta u - chi del & sdot; ((u)/v(k )del v) + ru - mu u(2), x is an element of Omega, 0 = Delta v - alpha v + beta u, x is an element of Omega, (1) under no-flux boundary conditions in a smoothly bounded domain Omega subset of R-n with n >= 3, the parameters chi, r, mu, alpha ,beta > 0 are positive constants and k is an element of (0, 1). In the past few years, there has been considerable interest in exploring whether logistic kinetics can sufficiently guarantee the global existence and boundedness of classical solutions or prevent finite-time blow-up in various chemotaxis models. In particular, significant results have been reported by numerous authors regarding system Eq. (1). For instance, a recent study (Kurt 2025) demonstrated that Eq. (1) admits a globally bounded classical solution provided that mu is sufficiently large and k < (1)/(2 )+ (1)/(n) with n >= 2. It is then natural to ask whether the boundedness of classical solutions of Eq. (1) can be established independently of the condition connecting k and n or considering a milder condition for mu. This paper addresses this question by providing an extension of the upper bound for k and a weaker condition for mu and proves that for all suitably smooth initial data and any given k is an element of (0, 1), Eq. (1) possesses a globally bounded classical solution if mu is suitably large such that mu > {beta chi (1/1-k) 2 (k/1-k )+ 4(2-k/1-k )beta(chi k)(1/1-k), n = 3, beta chi(1/1-k) ((n)/(2)) (k/1-k )+ 2 beta(chi k)(1/1-k )(2 + (4)/(n-2))(1/2)n(1/1-k), n >= 4.