论文标题
相变稳态到双曲线 - 抛物性系统建模血管网络的非线性稳定性
Nonlinear stability of phase transition steady states to a hyperbolic-parabolic system modelling vascular networks
论文作者
论文摘要
本文与趋化性聚集的准线性双曲线 - 抛物性系统的存在和稳定有关，该系统在\ cite {ambrosi2005Review，gamba2003 percolation}中提出，以描述相干的血管网络形成，以描述相干的血管网络形成。考虑到半行中的系统$ \ mathbb {r} _ {+} =（0，\ infty）$具有差异性边界条件，我们首先证明存在\ textColor {black black} {在某些压力功能上的某些结构条件下，非恒定相位过渡稳态的独特性以及非恒定相位过渡稳态的独特性。然后，我们证明这种独特的相变稳态在微小的扰动上是非线性渐近稳定的。我们通过能量估计方法，{\ it先验}假设的技术和加权强大的不等式的技术证明了结果。
This paper is concerned with the existence and stability of phase transition steady states to a quasi-linear hyperbolic-parabolic system of chemotactic aggregation, which was proposed in \cite{ambrosi2005review, gamba2003percolation} to describe the coherent vascular network formation observed {\it in vitro} experiment. Considering the system in the half line $ \mathbb{R}_{+}=(0,\infty)$ with Dirichlet boundary conditions, we first prove the existence \textcolor{black}{and uniqueness of non-constant phase transition steady states} under some structure conditions on the pressure function. Then we prove that this unique phase transition steady state is nonlinearly asymptotically stable against a small perturbation. We prove our results by the method of energy estimates, the technique of {\it a priori} assumption and a weighted Hardy-type inequality.
