论文标题
双曲线松弛近似的边界条件的构建II：JIN-XIN松弛模型
Construction of Boundary Conditions for Hyperbolic Relaxation Approximations II: Jin-Xin Relaxation Model
论文作者
论文摘要
这是我们在该系列中的第二项工作，内容涉及构造双曲线松弛近似的边界条件。目前的工作与一维线性化的JIN-XIN弛豫模型有关，这是一种具有非特征性边界双曲线保护定律的方便近似值。假设为保护法提供了适当的边界条件。我们为弛豫模型构建边界条件，期望由边界条件与给定的保护定律进行近似。构造的边界条件是高度非唯一的。分析了它们对广义Kreiss条件的满意度。研究了与初始数据的兼容性。此外，通过诉诸形式的渐近扩张，我们证明了近似值的有效性。
This is our second work in the series about constructing boundary conditions for hyperbolic relaxation approximations. The present work is concerned with the one-dimensional linearized Jin-Xin relaxation model, a convenient approximation of hyperbolic conservation laws, with non-characteristic boundaries. Assume that proper boundary conditions are given for the conservation laws. We construct boundary conditions for the relaxation model with the expectation that the resultant initial-boundary-value problems are approximations to the given conservation laws with the boundary conditions. The constructed boundary conditions are highly non-unique. Their satisfaction of the generalized Kreiss condition is analyzed. The compatibility with initial data is studied. Furthermore, by resorting to a formal asymptotic expansion, we prove the effectiveness of the approximations.
