双曲松弛近似的边界条件构造II：Jin-Xin松弛模型
Construction of Boundary Conditions for Hyperbolic Relaxation Approximations II: Jin-Xin Relaxation Model
摘要：
这是我们关于构造双曲松弛近似边界条件系列的第二篇工作。本文研究了一维线性化的Jin-Xin松弛模型，它是双曲守恒律方程的一个方便的近似，具有非特征边界。假定守恒律有适当的边界条件。我们构造的松弛模型的边界条件，期望由此产生的初边值问题的近似与边界条件的给定的守恒律。所构造的边界条件是高度非唯一的。分析了它们对广义Kreiss条件的满足情况。研究了与初始数据的相容性。此外，通过诉诸一个正式的渐近展开，我们证明了有效的近似。
英文摘要：
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.
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