双曲松弛近似边界条件的构造II: Jin-Xin松弛模型

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2022-03-08 DOI:10.1090/qam/1627

Xiaxia Cao, W. Yong

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引用次数: 0

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部作品。本文研究一维线性化的Jin-Xin松弛模型，这是一种具有非特征边界的双曲守恒律的方便近似。假设守恒律有适当的边界条件。我们构造了松弛模型的边界条件，期望得到的初边值问题是给定守恒律的近似。构造的边界条件是高度非唯一的。分析了它们对广义Kreiss条件的满足性。研究了与初始数据的相容性。进一步，通过形式渐近展开式，我们证明了近似的有效性。

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Construction of boundary conditions for hyperbolic relaxation approximations II: Jin-Xin relaxation model

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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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.