论文标题
全球存在用于依赖信号依赖性凯勒 - 塞格模型的弱解决方案，用于局部传感趋化性
Global Existence of Weak Solutions to a Signal-dependent Keller-Segel Model for Local Sensing Chemotaxis
论文作者
论文摘要
本文致力于全球存在弱解决方案，以实现以下趋化模型的趋化模型 \ begin {equation} \ begin {case} \ label {chemo0} u_t =δ（γ（v）u） τv_{t} =ΔV-v+u \ end {cases} \ end {equation}在具有无升边界条件的平滑界面域中。该问题具有积极的信号依赖性运动函数$γ（\ cdot）$，随着$ v $的无限，它可能消失。在本文中，我们首先修改了最近在\ cite {gm，gm2}中开发的比较方法，以在$γ（\ cdot）$的弱假设下得出$ v $的上限。然后，通过引入与比较方法兼容的合适近似方案，我们通过紧凑型参数在任何空间维度中建立了弱解的全局存在。我们的弱解决方案的规律性比以前的文献中获得的更高。
This paper is devoted to global existence of weak solutions to the following degenerate kinetic model of chemotaxis \begin{equation} \begin{cases}\label{chemo0} u_t=Δ(γ(v)u) τv_{t}=Δv-v+u \end{cases} \end{equation}in a smooth bounded domain with no-flux boundary conditions. The problem features a positive signal-dependent motility function $γ(\cdot)$ which may vanish as $v$ becomes unbounded. In this paper, we first modify the comparison approach developed recently in \cite{GM,GM2} to derive the upper bounds of $v$ under weakened assumptions on $γ(\cdot)$. Then by introducing a suitable approximation scheme which is compatible with the comparison method, we establish the global existence of weak solutions in any spatial dimension via compactness argument. Our weak solution has higher regularity than those obtained in previous literature.
