Global existence of solutions to the fully parabolic chemotaxis system with logistic source under nonlinear Neumann boundary conditions

2024/06/03 by Le, Minh
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.01826

Abstract

We study the existence of global boundedness solutions to the fully parabolic chemotaxis systems with logistic sources, ru- μu², under nonlinear Neumann boundary conditions, (∂ u)/(∂ ν)= |u|^p where p >1 in smooth bounded domain Ω⊂ ℝⁿ with n ≥ 2. A recent study by Le (2023) has shown that the logistic sources can ensure that solutions are global and bounded when n =2 with p < (3)/(2) and n=3 with p <(7)/(5). In this paper, we extend the previous findings by demonstrating the existence of global bounded solutions when p< (3)/(2) in any spatial dimension n ≥ 2.

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