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
Abstract:
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
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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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