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The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term

  • Author Bio: E-mail address: tong-li@uiowa.edu; E-mail address: ganyinxj@gmail.com
  • Lihui Guo, E-mail address: lihguo@126.com

    Lihui Guo, E-mail address: lihguo@126.com 
This work is partially supported by National Natural Science Foundation of China (11401508,11461066), China Scholarship Council, the Scientific Research Program of the Higher Education Institution of XinJiang (XJEDU2014I001).
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  • We study the vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term. The phenomena of concentration and cavitation to Chaplygin gas equations with a friction term are identified and analyzed as the pressure vanishes. Due to the influence of source term, the Riemann solutions are no longer self-similar. When the pressure vanishes, the Riemann solutions to the inhomogeneous Chaplygin gas equations converge to the Riemann solutions to the pressureless gas dynamics model with a friction term.

    Mathematics Subject Classification: Primary: 35L65, 35L67; Secondary: 76N15.


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  • Figure 3.1.  Riemann solution in the phase plane

    Figure 4.1.  Riemann solution when $(u_+, \rho_+)\in \rm{Ⅳ}(u_-, \rho_-).$

    Figure 4.2.  Riemann solution when $(u_+, \rho_+)\in \rm{Ⅰ}(u_-, \rho_-).$

    Figure 4.3.  Riemann solution when $(u_+, \rho_+)\in \rm{Ⅲ}(u_-, \rho_-).$

    Figure 4.4.  Riemann solution when $(u_+, \rho_+)\in \rm{Ⅱ}(u_-, \rho_-).$

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