论文标题
具有II型特征边界双曲线松弛系统的边界条件
Boundary Conditions for Hyperbolic Relaxation Systems with Characteristic Boundaries of Type II
论文作者
论文摘要
本文是我们对双曲线放松系统的上一项工作的延续。在这里，我们着重于II型的特征边界，其中边界是平衡系统的特征，并且是放松系统的非特征。对于这种特征性的初始符合价值问题（IBVP），我们引入了三尺度的渐近扩展，以分析一般多维线性宽松系统的边界层行为。此外，我们通过诉诸某些微妙的基质变换和线性操作员的扰动理论来得出降低的边界条件。事实证明，还原的边界条件满足了特征性IBVP的均匀的Kreiss条件。通过涉及傅立叶宽带变换和基于结构稳定性条件的能量方法的误差估计来显示其有效性。
This paper is a continuation of our preceding work on hyperbolic relaxation systems with characteristic boundaries of type I. Here we focus on the characteristic boundaries of type II, where the boundary is characteristic for the equilibrium system and is non-characteristic for the relaxation system. For this kind of characteristic initial-boundary-value problems (IBVPs), we introduce a three-scale asymptotic expansion to analyze the boundary-layer behaviors of the general multi-dimensional linear relaxation systems. Moreover, we derive the reduced boundary condition under the Generalized Kreiss Condition by resorting to some subtle matrix transformations and the perturbation theory of linear operators. The reduced boundary condition is proved to satisfy the Uniformed Kreiss Condition for characteristic IBVPs. Its validity is shown through an error estimate involving the Fourier-Laplace transformation and an energy method based on the structural stability condition.
