CHARACTERISTIC DECOMPOSITIONS FOR
THE UNSTEADY TRANSONIC SMALL
DISTURBANCE EQUATION

Abstract

We consider a Riemann problem for the unsteady transonic small disturbance equation resulting in interacting rarefaction waves. We rewrite the problem in self-similar coordinates and we derive characteristic decomposition equations for the inclination angle variables.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 1
Year: 2019

DOI: 10.12732/ijam.v32i1.6

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] S. Chen, A. Qu, Interaction of rarefaction waves in jet stream, J. Differential Equations, 248 (2010), 2931-2954.
  2. [2] X. Chen, Y. Zheng, The interaction of rarefaction waves of the twodimensional Euler system, Indiana University Mathematics Journal, 59(1) (2010), 231-256.
  3. [3] Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Rational Mech. Anal., 155 (2000), 277-298.
  4. [4] J. Ge, W. Sheng, The two dimensional gas expansion problem of the Euler equations for the generalizes Chaplygin gas, Comm. Pure and Applied Analysis, 13(6) (2014), 2733-2748.
  5. [5] Y. Hu, J. Li, W. Sheng, Degenerate Goursat-type boundary value problems arising from the study of two-dimensional isothermal Euler equations, Z. Angew. Math. Phys., (2012) Springer Basel AG.
  6. [6] Y. Hu, G. Wang, The interaction of rarefaction waves of a two-dimensional nonlinear wave system, Nonlinear Analysis: Real World Applications, 22 (2015), 1-15.
  7. [7] I. Jegdi´c, K. Jegdi´c, Properties of solutions in semi-hyperbolic patches for unsteady transonic small disturbance equations, Electronic Journal of Differential Equations, 2015 No. 243 (2015), 1-20.
  8. [8] I. Jegdi´c, K. Jegdi´c, Interacting rarefaction waves for the unsteady transonic small disturbance equation, Electronic Journal of Differential Equations, 2016 No. 248 (2016), 1-15
  9. [9] B. L. Keyfitz, Self-similar solutions of two-dimensional conservation laws, J. Hyp. Diff. Eq., 1 (2004), 445-492.
  10. [10] J. Li, On the two-dimensional gas expansion for compressible Euler equations, SIAM J. Appl. Math., 62(3) (2001), 831-852.
  11. [11] J. Li, T. Zhang. Y. Zheng, Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations, Comm. Math. Phys., 267 (2006), 1-12.
  12. [12] J. Li, Y. Zheng, Interaction of rarefaction waves of the two-dimensional self-similar Euler equations, Arch. Rational Mech Anal., 193 (2009), 632657.
  13. [13] J. Li, Z. Yang, Y. Zheng, Characteristic decompositions and interaction of rarefaction waves of 2-D Euler equations, J. Differential Equations, 250 (2011), 782-798.
  14. [14] H. Yang, T. Zhang, On two-dimensional gas expansion for pressuregradient equations of Euler system, J. Math. Anal. Appl., 298 (2004), 523-537.
  15. [15] Y. Zheng, The compressible Euler system in two dimensions, In: Contemporary Applied Mathematics, World Scientific and the Higher Education Press, Lecture Notes of 2007 Shanghai Mathematics Summer School.