Electron. J. Differential Equations, Vol. 2016 (2016), No. 248, pp. 1-15.

Interacting rarefaction waves for the unsteady transonic small disturbance equation

Ilija Jegdic, Katarina Jegdic

We consider a Riemann problem for the unsteady transonic small disturbance equation that results in two rarefaction waves. We write the problem in self-similar and parabolic coordinates and we obtain a system that changes type from hyperbolic to elliptic. We use the characteristic decomposition equations to study the complicated interaction of these two rarefaction waves in the hyperbolic region. We obtain local existence of the solution and we derive various properties of the solution and of the characteristic curves.

Submitted November 16, 2015. Published September 14, 2016.
Math Subject Classifications: 35L65.
Key Words: Unsteady transonic small disturbance; mixed type system; rarefaction waves; shocks.

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Ilija Jegdic
Department of Mathematics
Texas Southern University
3100 Cleburne Street
Houston, TX 77004, USA
email: ilija.jegdic@tsu.edu
Katarina Jegdic
Department of Mathematics and Statistics
University of Houston - Downtown
1 Main St, Houston, TX 77002, USA
email: jegdick@uhd.edu

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