Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (6): 2274-2282.doi: 10.1007/s10473-024-0612-2

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THE CONVERGENT RATE OF VISCOSITY METHOD FOR A VARIANT NON-ISENTROPIC SYSTEM OF POLYTROPIC GAS

Lijuan CHEN1, Xianting WANG2,†, Changfeng XUE1   

  1. 1. School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng 224051, China;
    2. Wuxi Institute of Technology, Wuxi 214121, China
  • Received:2023-08-14 Accepted:2024-05-01 Published:2024-12-06
  • Contact: † Xianting WANG, E-mail: wangxt@wxit.edu.cn
  • About author:Lijuan CHEN, E-mail: chenlijuan@ycit.cn; Changfeng XUE, E-mail: cfxue@ycit.edu.cn
  • Supported by:
    National Natural Science Foundation of China (12071409).

Abstract: In this short paper, we remove the restriction $\gamma \in (1,3]$ that was used in the paper "The rate of convergence of the viscosity method for a nonlinear hyperbolic system" (Nonlinear Analysis, 1999, 38: 435-445) and obtain a global Hölder continuous solution and the convergent rate of the viscosity method for the Cauchy problem of the variant non-isentropic system of polytropic gas for any adiabatic exponent $\gamma>1$.

Key words: Hölder continuous solution, nonlinear hyperbolic system, viscosity solution, convergent rate, maximum principle

CLC Number: 

  • 35L03
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