Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Maximal attractor for the system of one-dimensional polytropic viscous ideal gas


Authors: Songmu Zheng and Yuming Qin
Journal: Quart. Appl. Math. 59 (2001), 579-599
MSC: Primary 35B41; Secondary 35B30, 35B40, 35L65, 37L30, 76D03
DOI: https://doi.org/10.1090/qam/1848536
MathSciNet review: MR1848536
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Abstract: In this paper, the dynamics for the system of polytropic viscous ideal gas is investigated. One of the important features of this problem is that the metric spaces $ {H^{\left( 1 \right)}}$ and $ {H^{\left( 2 \right)}}$ that we work with are two incomplete metric spaces, as can be seen from the constraints $ \theta > 0$ and $ u > 0$ with $ \theta $ and $ u$ begin absolute temperature and specific volume, respectively. For any constants $ {\beta _1}, {\beta _2}, {\beta _3}, {\beta _4}, {\beta _5}$ satisfying certain conditions, two sequences of closed subspaces $ H_\beta ^{\left( i \right)} \subset {H^{\left( i \right)}} \left( i = 1, 2 \right)$ are found, and the existence of two maximal (universal) attractors in $ H_\beta ^{\left( 1 \right)}$ and $ H_\beta ^{\left( 2 \right)}$ is proved.


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DOI: https://doi.org/10.1090/qam/1848536
Article copyright: © Copyright 2001 American Mathematical Society


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