论文标题
奇数凯勒 - 塞格模型的径向边界层
Radial boundary layers for the singular Keller-Segel model
论文作者
论文摘要
本文涉及径向溶液的扩散极限（作为$ \ va \ rightarrow 0 $），趋化溶液在具有对数奇异灵敏度的趋化溶液中，在有界的间隔内具有混合的dirichlet和罗宾边界条件。我们使用Cole-Hopf类型转换来解决对数奇点，并证明转换系统的解决方案的边界层配置文件为$ \ va \ to 0 $，其中边界层的厚度为$ \ Mathcal {o}（O}（\ va^α）（\ Va^α）$，带有$ 0 <α<α<α<α<α<\ frac} = {1} $} = 2}通过通过Cole-HOPF转换将结果转移回原始的趋化模型，我们发现边界层曲线存在于溶液的梯度上，并且相对于$ \ va> 0 $，溶液本身均匀收敛。
This paper is concerned with the diffusion limit (as $\va\rightarrow 0$) of radial solutions to a chemotaxis system with logarithmic singular sensitivity in a bounded interval with mixed Dirichlet and Robin boundary conditions. We use a Cole-Hopf type transformation to resolve the logarithmic singularity and prove that the solution of the transformed system has a boundary-layer profile as $\va \to 0$, where the boundary layer thickness is of $\mathcal{O}(\va^α)$ with $0<α<\frac{1}{2}$. By transferring the results back to the original chemotaxis model via Cole-Hopf transformation, we find that boundary layer profile is present at the gradient of solutions and the solution itself is uniformly convergent with respect to $\va>0$.
