Time:14:00-15:00, Wednesday, October 29 2025

Venue: E4-201, Yungu Campus

Speaker: Le Hoang Minh, Westlake University

Title: Boundedness In Chemotaxis System With General Weak Singular Sensitivity And Logistic Sources

Abstract: We consider the following system in an open, bounded domain \( \Omega \subset \mathbb{R}^n \) with \( n \geq 2 \):

\begin{equation*}

\begin{cases}

u_t &= \Delta u - \nabla \cdot (u \chi(v) \nabla v) + ru - \dfrac{\mu u^2}{\ln^\gamma(u+e)}, \\

\kappa v_t &= \Delta v - \alpha v + \beta u,

\end{cases}

\end{equation*}

where \( \chi(\cdot) \in C^1((0, \infty)) \) is positive, \( r, \mu, \alpha, \beta > 0 \), \( \kappa \in \{0, 1\} \), and \( \gamma \geq 0 \). We introduce the concept of a weak singular sensitivity condition and show that if \( \chi \) satisfies this condition, then solutions are global and bounded. Furthermore, when \( \kappa = 0 \) and \( \chi(v) = \dfrac{\chi_0}{v} \) for some \( \chi_0 > 0 \), \textcolor{red}{solutions remain globally bounded provided $ {\chi_0} < \min \left\{ \dfrac{1}{2}, \dfrac{2}{n} \right\} $}.

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