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Initial-Boundary Value Problems for One-Dimensional pth Power Viscous Reactive Gas with Density-Dependent Viscosity

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Abstract

Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value/Cauchy problem of the one-dimensional pth power viscous reactive gas with positive constant viscosity, no result is available up to now for the corresponding problems with density-dependent viscosity. The main purpose of this paper is to study the global existence and asymptotic behavior of solutions to three types of initial-boundary value problems of 1d pth power viscous reactive gas with density-dependent viscosity and large initial data. The key ingredient in our analysis is to deduce the positive lower and upper bounds on both the specific volume and the absolute temperature.

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The data that support the findings of this study are available from the author on reasonable request.

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Acknowledgements

This research is supported by National Natural Science Foundation of China (Grant No. 12101579), the Natural Science Foundation of Hubei Province, China (Grant No. 2021CFB022), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan, Grant No. CUGST2).

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Authors and Affiliations

  1. Center for Mathematical Sciences, China University of Geosciences, Wuhan, 430074, China

    Yongkai Liao

  2. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Yongkai Liao

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Communicated by Gui-Qiang G. Chen

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Liao, Y. Initial-Boundary Value Problems for One-Dimensional pth Power Viscous Reactive Gas with Density-Dependent Viscosity. J. Math. Fluid Mech. 26, 14 (2024). https://doi.org/10.1007/s00021-023-00846-z

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