Boundedness in a chemotaxis system with weakly singular sensitivity in dimension two with arbitrary sub-quadratic degradation sources

2024/05/07 by Le, Minh · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.04666

Abstract

We study the global existence and boundedness of solutions to a chemotaxis system with weakly singular sensitivity and sub-logistic sources in a two dimensional domain. X. Zhao (Nonlinearity; 2023; 36; 3909-3938 ) showed that the logistic degradation, -μu², can prevent blow-up under the largeness assumption on μ. In this paper, we improve the result by replacing the quadratic degradation by sub-logistic one, -(μu²)/(ln^β(u+e)) with β∈ (0,1), and removing the largeness assumption on μ.

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• An improvement toward global boundedness in a fully parabolic chemotaxis with singular sensitivity in any dimension

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