平衡律非齐次系统的相对熵法

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2020-08-18 DOI:10.1090/qam/1577

C. Christoforou

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引用次数: 1

摘要

在相对熵的背景下，研究了在所有本构函数中具有空间和时间不均匀性的平衡律的一般双曲系统。在这种情况下开发了一个框架，该框架有助于测度值弱唯一性与强唯一性定理、粘性解的稳定性定理和粘性参数趋于零时的收敛定理。本文的主要目标是提出相对熵框架仍然可以应用的假设。给出了具有不同特征的不均匀性系统的例子，并在每个例子的设置中讨论了假设。

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The relative entropy method for inhomogeneous systems of balance laws

General hyperbolic systems of balance laws with inhomogeneity in space and time in all constitutive functions are studied in the context of relative entropy. A framework is developed in this setting that contributes to a measure-valued weak vs. strong uniqueness theorem, a stability theorem of viscous solutions and a convergence theorem as the viscosity parameter tends to zero. The main goal of this paper is to develop hypotheses under which the relative entropy framework can still be applied. Examples of systems with inhomogeneity that have different characteristics are presented and the hypotheses are discussed in the setting of each example.

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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.