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arXiv · 2405.04666

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

Minh Le
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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, $-μu^2$, 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, $-\frac{μu^2}{\ln^β(u+e)}$ with $β\in (0,1)$, and removing the largeness assumption on $μ$.

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Minh Le. 2024-05-07. Boundedness in a chemotaxis system with weakly singular sensitivity in dimension two with arbitrary sub-quadratic degradation sources. https://arxiv.org/abs/2405.04666

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