一维奇异趋化–消耗系统古典解的整体有界性

Global Boundedness of Solutions to a Chemotaxis-Consumption Systems with Singular Sensitivity in Dimension One

摘要: 本文研究在齐次Neumann边界条件下的具有奇异敏感性的趋化系统：$u_t=u_{xx}-\chi {\left(\frac{u}{v^{\alpha }}{v}_x\right)}_x$ ，$v_t=v_{xx}-u{v}^{\beta }$ ，其中$\chi >0$ 。在一维情形下，当$\beta >\frac{1}{2}$ 及$\alpha \in \left(0,\min \left\{1,\frac{\beta +1}{2}\right\}\right]$ 时，系统存在整体有界的古典解。

Abstract: This paper deals with a chemotaxis system with singular sensitivity under homogeneous Neumann boundary condition: $u_t=u_{xx}-\chi {\left(\frac{u}{v^{\alpha }}{v}_x\right)}_x$ , $v_t=v_{xx}-u{v}^{\beta }$ with $\chi >0$ . Under one-dimensional setting, if $\beta >\frac{1}{2}$ and $\alpha \in \left(0,\min \left\{1,\frac{\beta +1}{2}\right\}\right]$ , the system admits globally bounded classical solutions.