Ayazoglu, Rabil2024-10-042024-10-0420220022-247X1096-0813https://doi.org/10.1016/j.jmaa.2022.126482http://hdl.handle.net/20.500.12403/3352This paper deals with the higher dimension quasilinear parabolic-parabolic Keller-Segel system involving a source term of variable logistic type u(t) = del . (phi(u)del u) - del. (phi(u)del upsilon) + g(x, u), -Delta upsilon = -upsilon + u, in (x, t) is an element of Omega x (0, T), subject to nonnegative initial data and homogeneous Neumann boundary condition, where Omega is a smooth and bounded domain in R-N(N >= 1) and g is an element of C-1 ((Omega) over bar x [0, infinity)) function satisfies g(x, s) <= eta(sk(x)) - mu s(m(x)), s > 0 with g(x, 0) >= 0, x is an element of Omega and eta >= 0, mu > 0 are constants, k, m are measurable functions with 1 < k(-) := ess(x is an element of Omega) infk (x) <= k(x) <= k(+) := ess sup(x is an element of Omega) k(x)< +infinity, 2 <= m(-) := ess(x is an element of Omega) infm (x) <= m(x) <= m(+) := ess sup(x is an element of Omega) m(x)< +infinity. Positive functions psi, phi is an element of C-2(inverted right perpendicular0, infinity)) satisfy nu s(q) <= phi <= chi(sq) and phi >= sigma s(p) with p, q is an element of R, nu, chi, sigma > 0 when s >= 0. It is proved that if q = m(-) - 1 (critical case) and mu > chi (1 - 2/N (m(-) - p - 1)(+), then there exists a classical solution which is global in time and bounded. Moreover, if q is an element of (k(+) - 1, m(-) - 1), we obtain that there is a classical solution of the above system uniformly in time bounded without any restrictions on m(-) and mu. (c) 2022 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessChemotaxisBoundednessVariable logistic sourceArticle516110.1016/j.jmaa.2022.1264822-s2.0-85134328263Q1WOS:000911439700013Q2