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AIMS Mathematics

2021, Volume 6, Issue 6: 6482-6489. doi: 10.3934/math.2021381
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Research article

Cauchy problem for isothermal system in a general nozzle with space-dependent friction

  • 1.
    K. K. Chen Institute for Advanced Studies, Hangzhou Normal University, China
  • 2.
    Wuxi Institute of Technology, China
  • 3.
    School of Mathematics and Statistics, Universidad Pedagógica y Tecnológica de Colombia, Colombia
  • Received: 08 February 2021 Accepted: 09 April 2021 Published: 15 April 2021

  • MSC : 35L65, 76N10

  • In this paper, we study the Cauchy problem of the isothermal system in a general nozzle with space-dependent friction . First, by using the maximum principle, we obtain the uniform bound , , independent of the time, of the viscosity-flux approximation solutions; Second, by using the compensated compactness method coupled with the convergence framework given in [5], we prove that the limit, of , as go to zero, is a uniformly bounded entropy solution.

    Citation: Yun-guang Lu, Xian-ting Wang, Richard De la cruz. Cauchy problem for isothermal system in a general nozzle with space-dependent friction[J]. AIMS Mathematics, 2021, 6(6): 6482-6489. doi: 10.3934/math.2021381

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  • In this paper, we study the Cauchy problem of the isothermal system in a general nozzle with space-dependent friction . First, by using the maximum principle, we obtain the uniform bound , , independent of the time, of the viscosity-flux approximation solutions; Second, by using the compensated compactness method coupled with the convergence framework given in [5], we prove that the limit, of , as go to zero, is a uniformly bounded entropy solution.




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