Akademik Veri Yönetim Sistemi
JOURNAL OF DIFFERENTIAL EQUATIONS, cilt.416, ss.1429-1461, 2025 (SCI-Expanded)
This paper deals with the following parabolic-elliptic chemotaxis competition system with weak singular sensitivity and logistic source {ut=Delta u-chi del center dot(u/v(lambda)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, partial derivative u/partial derivative nu=partial derivative v/partial derivative nu=0, x is an element of partial derivative Omega, (0.1) where Omega subset of R-N(N >= 1) is a smooth bounded domain, the parameters chi,r,mu,alpha,beta are positive constants and lambda is an element of(0,1). It is well known that for parabolic-elliptic chemotaxis systems including singularity, a uniform-in-time positive pointwise lower bound for v is vitally important for establishing the global boundedness of classical solutions since the cross-diffusive term becomes unbounded near v=0. To this end, a key step in the literature is to establish a proper positive lower bound for the mass functional integral(Omega)u, which, due to the presence of logistic kinetics, is not preserved and hence it turns in for v. In contrast to this approach, in this article, the boundedness of classical solutions of (0.1) is obtained without using the uniformly positive lower bound of v. Among others, it has been proven that without establishing a uniform-in-time positive pointwise lower bound for v, if lambda is an element of(0,1), then there exists mu>mu* such that for all suitably smooth initial data, L-p-norm (for any p >= 2) of any globally defined positive solution is bounded; moreover, problem (0.1) possesses a unique globally defined classical solution. In addition, the solutions are shown to be uniformly bounded under the additional assumption lambda<1/2+1/N with N >= 2. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.